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PSLE

PSLE Foundation Mathematics

<p>The diagram shows sphere with centre $O$ and a total surface area of $\frac{192\pi}{3}$ $\text{cm}^2$. Vertices of an equilateral triangle $ABC$ are on the surface of the sphere. Given that&nbsp;$AB = 2$ $\text{cm}$, find</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">the total surface area of pyramid $O-ABC$,</div></li><li><div class="list-item-paragraph">the volume of pyramid $O-ABC$, leaving your answers in the exact form.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770522016003-tj1ptowyk1h.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA1MjIwMTYwMDMtdGoxcHRvd3lrMWgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.88fMWGFJf0r9xPsPfxlhUmq5hUtPIBt_rbVX3e-Fa5Y" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram shows sphere with centre $O$ and a total surface area of $\frac{192\pi}{3}$ $\text{cm}^2$. Vertices of an equilateral triangle $ABC$ are on the surface of the sphere. Given that $AB = 2$ $\text{cm}$, find

Volume and Surface Area of Pyramids

Volume and Surface Area of Spheres

Pythagoras’ Theorem in Three Dimensions

IP2U11 HOT Q4

Mensuration (Pyramid, Cones and Spheres)

Pythagoras’ Theorem

<p>The diagram shows a solid $ABCDEF$, where the base $ABCD$ is a square, $DE$ and $BF$ are perpendicular to the plane $ABCD$. Given that&nbsp;$AB = DE = 2BF = 2$, find the exact volume of the solid $ABCDEF$.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770521325143-zw4jig8cse.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA1MjEzMjUxNDMtenc0amlnOGNzZS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODUwODEzLCJleHAiOjE3OTI4NTExMTN9.8P5VMapzaUacHP545f4uk0K0B-jjDuiK43IpFZ0X69Q" style="max-width: min(220px, 100%); height: auto; display: block;" alt="Solid ABCDEF with square base ABCD" class="alignright custom-width" /></figure></div>

The diagram shows a solid $ABCDEF$, where the base $ABCD$ is a square, $DE$ and $BF$ are perpendicular to the plane $ABCD$. Given that $AB = DE = 2BF = 2$, find the exact volume of the solid $ABCDEF$.

IP2U11 HOT Q3

<p>The diagram shows a solid $ABCDE$, where&nbsp;$AE$ and $CD$ are perpendicular to the plane $ABC$. Given that&nbsp;$AE = 2CD = 2$ cm, $CA = CB = 3$ cm and $AB = 2\sqrt{5}$ cm, find the exact volume of the solid $ABCDE$.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770520793503-7156h958mrf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA1MjA3OTM1MDMtNzE1Nmg5NThtcmYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.HDRTAJ8XQiPMKarxt1BUOxWE353TL2vTNUR3zFQU6Mg" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

The diagram shows a solid $ABCDE$, where $AE$ and $CD$ are perpendicular to the plane $ABC$. Given that $AE = 2CD = 2$ cm, $CA = CB = 3$ cm and $AB = 2\sqrt{5}$ cm, find the exact volume of the solid $ABCDE$.

IP2U11 HOT Q2

<p>The iron solid is made up of a hemisphere joined to a cylinder with a radius of $6$ cm and a height of $10$ cm as shown.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">Calculate</div><ol class="i-list"><li><div class="list-item-paragraph">the total volume of the solid, </div></li><li><div class="list-item-paragraph">the total surface area of the solid.</div></li></ol></li><li><div class="list-item-paragraph">If the solid is melted to form a pyramid of a base area of $250$ cm$^{2}$, find the height of the pyramid.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765260054310-ofpdiqfhk2i.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUyNjAwNTQzMTAtb2ZwZGlxZmhrMmkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.TqgSC0_3ba3f1dOMfpTzkTgp2aVDgu-foMt_AGXVd9A" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The iron solid is made up of a hemisphere joined to a cylinder with a radius of $6$ cm and a height of $10$ cm as shown.

Volume and Surface Area of Composite Solids

Conservation of Volume and Displacement

Composite Solid: Hemisphere Joined to a Cylinder

<p>The figure below is a pyramid with a square base of side $x$ cm and height $12$ cm.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p style="text-align: left">Given that its volume is $196$ cm$^{3}$, find</p><ol class="abc-list"><li data-list-item-id="item-1778404218846-srolr2gkb" data-list-item-path="item-1778404218846-srolr2gkb"><div class="list-item-paragraph">the value of $x$,</div></li><li data-list-item-id="item-1778404219514-j8fopq2wy" data-list-item-path="item-1778404219514-j8fopq2wy"><div class="list-item-paragraph">the total surface area.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765194644521-g9el86i055p.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTQ2NDQ1MjEtZzllbDg2aTA1NXAucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.dIbq13TEFaK8ZAYRD4lrByIpVTSK06TTbyVIR20w1Ac" style="max-width: min(170px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>
<p>Assume the apex is vertically above the centre of the square base (a right square-based pyramid). This condition is needed for the stated surface-area and height calculations.</p>

The figure below is a pyramid with a square base of side $x$ cm and height $12$ cm.

Assume the apex is vertically above the centre of the square base (a right square-based pyramid). This condition is needed for the stated surface-area and height calculations.

Square-Based Pyramid: Finding Missing Dimensions and Surface Area

<p>A pyramid is made of a square base and four equilateral triangles.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The square has sides of $10$ cm.</p><p>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">the area of one triangular face of the pyramid,</div></li><li><div class="list-item-paragraph">the total surface area of the pyramid.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765194400393-kzu2in1j7y.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTQ0MDAzOTMta3p1MmluMWo3eS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODUwODEzLCJleHAiOjE3OTI4NTExMTN9.qjELf5dsFTy03wSgfWm-HQ89QfCB02lURshJ3CHQe4w" style="max-width: min(220px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

A pyramid is made of a square base and four equilateral triangles.

Surface Area of a Pyramid with Equilateral Triangular Faces

<p>The diagram shows a solid square-based pyramid with a slant height of $17$ cm. The square has sides of $16$ cm.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p style="text-align: left">Find</p><ol class="abc-list"><li data-list-item-id="item-1778403934889-ihjr4aagl" data-list-item-path="item-1778403934889-ihjr4aagl"><div class="list-item-paragraph">the total surface area, </div></li><li data-list-item-id="item-1778403935350-h4ucmkyro" data-list-item-path="item-1778403935350-h4ucmkyro"><div class="list-item-paragraph">the height,</div></li></ol><p style="text-align: left">of the pyramid.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765194236986-1riby58rm9k.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTQyMzY5ODYtMXJpYnk1OHJtOWsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.UpAHhwscVBwj4hy08a9Zgj6L4JWZTMOv0q3PlQHifVk" style="max-width: min(220px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>
<p>Assume the apex is vertically above the centre of the square base (a right square-based pyramid). This condition is needed for the stated surface-area and height calculations.</p>

The diagram shows a solid square-based pyramid with a slant height of $17$ cm. The square has sides of $16$ cm.

Slant Height of a Square Pyramid – Surface Area & Height

<p>A solid right pyramid has a square base with side $12$ cm and height $13$ cm.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">the volume,</div></li><li><div class="list-item-paragraph">the total surface area,</div></li></ol><p>of the pyramid.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765193852617-bjjoeh9yscp.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTM4NTI2MTctYmpqb2VoOXlzY3AucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.exEKzwVjvNv8-lfsitqfmZ9Hz3nQgvsbD-kWf_EaZgQ" style="max-width: min(240px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

A solid right pyramid has a square base with side $12$ cm and height $13$ cm.

Volume and Surface Area of a Square-Based Pyramid

<p>The volume of a solid square pyramid is $294$ cm$^{3}$. The height, $h$, of the pyramid is $18$ cm.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">Find the area of the square base.</div></li><li><div class="list-item-paragraph">Find the length of the square base.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765193471227-mj7ndx1qr8e.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTM0NzEyMjctbWo3bmR4MXFyOGUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.fLGy9fDAg37mKFTxpCHe_eeP_qxNQUiyEgLAszRaU9w" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The volume of a solid square pyramid is $294$ cm$^{3}$. The height, $h$, of the pyramid is $18$ cm.

Volume of a Pyramid – Determining the Base Length

<p>The diagram shows a solid square-based pyramid.</p>
<p>Given that the volume of the pyramid is $1280$ cm$^{3}$, find the height, $h$, of the pyramid.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765193240879-abwmd1kc9jk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTMyNDA4NzktYWJ3bWQxa2M5amsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.NsXhuGABh7Fv47mcOYmmGoVQphNTTfj6X62JVNINuXU" style="max-width: min(180px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

The diagram shows a solid square-based pyramid.

Given that the volume of the pyramid is $1280$ cm$^{3}$, find the height, $h$, of the pyramid.

Pyramid Height from Volume and Base Dimensions

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">Given that the height of the pyramid $VN=8$ cm, the length of $AB$ is $12$ cm and point $N$ is the centre of the square base $ABCD$. Find the volume of the square pyramid.</div></li><li><div class="list-item-paragraph">Find $VM$, the height of triangle $VBC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765193042333-vogcw36esqq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTMwNDIzMzMtdm9nY3czNmVzcXEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.SLAqxL7RMhHJGR1puCXk3lQnP9CU-v-_yR_Ct-LkxvM" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Square Pyramid with Internal Triangle: Volume & $VM$

<p>Below is a square based pyramid with a base area of $2$m$^{2}$ and a height of $1.8$m. Find the volume of the pyramid.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765192766734-s67uurbsql.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTI3NjY3MzQtczY3dXVyYnNxbC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODUwODEzLCJleHAiOjE3OTI4NTExMTN9.Y5Pm86KUtfaGcIDg8yt2oC2wzHN3Fn59k3PA4DPOmow" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

Below is a square based pyramid with a base area of $2$m$^{2}$ and a height of $1.8$m. Find the volume of the pyramid.

Square Pyramid Volume Calculation

<p>A triangular pyramid with a base area of $0.5$m$^{2}$ and a height of $0.7$m. Find the volume of the triangular pyramid.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765192500821-6d5lcbsbefk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTI1MDA4MjEtNmQ1bGNic2JlZmsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.PtrfQWAjRprDs6oS5eBpyCkSmD6mpfuC3BAxcl57t2Y" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

A triangular pyramid with a base area of $0.5$m$^{2}$ and a height of $0.7$m. Find the volume of the triangular pyramid.

Finding the Volume of a Pyramid from Base Area and Height

<p>The diagram shows a closed square-based pyramid with sides $10$ cm and height $12$ cm.<br>Find the</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">volume of the pyramid.</div></li><li><div class="list-item-paragraph">total surface area of the pyramid.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765192263219-9y2zmape2cb.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTIyNjMyMTktOXkyem1hcGUyY2IucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDgxMywiZXhwIjoxNzkyODUxMTEzfQ.8lpqt_CDsCPWQjdfRIhbmgFyFqCg_W59KE_svAqyzVI" style="max-width: min(160px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram shows a closed square-based pyramid with sides $10$ cm and height $12$ cm.
Find the

Surface Area of Pyramid

<p>A right pyramid with square base of side $3$ cm has a volume of $35$ cm$^{3}$.<br>Calculate the height of the pyramid.<br></p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765192072618-sle4ixppkj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTIwNzI2MTgtc2xlNGl4cHBrai5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODUwODEzLCJleHAiOjE3OTI4NTExMTN9.6ngj72uobUJdGWSItr4vN1AuiEJUAzuw1DnGVIHeb-Q" style="max-width: min(150px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

A right pyramid with square base of side $3$ cm has a volume of $35$ cm$^{3}$.
Calculate the height of the pyramid.


Finding Unknowns Given the Volume of Pyramid

<p>A pentagonal pyramid with a base area of $60$cm$^{2}$ and a height of $7$cm. Find the volume of the pentagonal pyramid.</p>
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A pentagonal pyramid with a base area of $60$cm$^{2}$ and a height of $7$cm. Find the volume of the pentagonal pyramid.

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