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PSLE Foundation Mathematics

<p>A cylindrical solid has a hemispherical top of the same radius $r\text{ cm}$. The cylinder has height $2r\text{ cm}$, and the volume of the entire solid is $576\pi\text{ cm}^3$.</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/1789189430874-y1vjytfj43.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODkxODk0MzA4NzQteTF2anl0Zmo0My5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODUxMDg3LCJleHAiOjE3OTI4NTEzODd9.QzOOaUKWE0CHjjawIYn4riJQpCfvOFtGZqB6Q9RAbR4" style="max-width: min(150px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="sec4-em-2025-mgs-s-p2-q7-b3-i1" data-list-item-path="sec4-em-2025-mgs-s-p2-q7-b3-i1"><div class="list-item-paragraph">Show that&nbsp;$r=6$.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="sec4-em-2025-mgs-s-p2-q7-b3-i2" data-list-item-path="sec4-em-2025-mgs-s-p2-q7-b3-i2"><div class="list-item-paragraph">The entire solid is melted to form a solid cone whose radius and height are equal. Find the total surface area of the cone.<span class="inline-marks">[4]</span></div></li></ol>

A cylindrical solid has a hemispherical top of the same radius $r\text{ cm}$. The cylinder has height $2r\text{ cm}$, and the volume of the entire solid is $576\pi\text{ cm}^3$.

The entire solid is melted to form a solid cone whose radius and height are equal. Find the total surface area of the cone.

Volume and Surface Area of Cylinders

Applications of Pythagoras’ Theorem

Volume and Surface Area of Spheres

Volume and Surface Area of Cones

Volume and Surface Area of Composite Solids

2025 MGS(S) PRELIMS P2 Q7

Volume and Surface Area of Prisms

Mensuration (Pyramid, Cones and Spheres)

Pythagoras’ Theorem

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA1MjIwMTYwMDMtdGoxcHRvd3lrMWgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MTA4NywiZXhwIjoxNzkyODUxMzg3fQ.oVthSn2_uLlr_unadWzqPXCdh_axSEfxvX7MeZUzjqY" 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

Pythagoras’ Theorem in Three Dimensions

IP2U11 HOT Q4

<p>The total surface area of the solid hemisphere below is $144$ cm$^{2}$.</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 radius,</div></li><li><div class="list-item-paragraph">the volume,</div></li></ol><p>of the hemisphere. </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/1778405912522-12lhpy1s5szq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Nzg0MDU5MTI1MjItMTJsaHB5MXM1c3pxLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI4NTEwODcsImV4cCI6MTc5Mjg1MTM4N30.TxvapdtOT9G-rMJwLHxa__-7-DtoSinH93IvHYRbVHY" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The total surface area of the solid hemisphere below is $144$ cm$^{2}$.

Total Surface Area and Volume of a Hemisphere

<p>A spherical metal ball has a surface area of $81\pi $cm$^{2}$. Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">its radius,</div></li><li><div class="list-item-paragraph">the mass of $51$ identical metal balls if they are made of metal of density $6.85$g/cm$^{3}$.</div></li></ol>

A spherical metal ball has a surface area of $81\pi $cm$^{2}$. Find

Sphere Calculation Involving Surface Area and Mass

<p>A spherical marble ball has a surface area of $2.78$ cm$^{2}$. Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">its radius,</div></li><li><div class="list-item-paragraph">the mass of $150$ identical marble balls if they are made of glass of density $2.57$g/cm$^{3}$. </div></li></ol>

A spherical marble ball has a surface area of $2.78$ cm$^{2}$. Find

Surface Area and Density Application of a Sphere

<p>A spherical tennis ball has a radius of $6.6$ cm.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the volume,</div></li><li><div class="list-item-paragraph">the surface area,</div></li></ol>
<p>of the tennis ball.</p>

A spherical tennis ball has a radius of $6.6$ cm.

Finding the Volume and Surface Area of a Tennis Ball

<p>A spherical basketball has a radius of $37.5$ cm.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the volume,</div></li><li><div class="list-item-paragraph">the surface area,</div></li></ol>
<p>of the basketball.</p>

A spherical basketball has a radius of $37.5$ cm.

Mensuration of a Sphere

<p>The outer curved surface area of a hemispherical bowl is painted with $87\pi $cm$^{2}$ of red paint. Find the radius of this bowl.</p>

The outer curved surface area of a hemispherical bowl is painted with $87\pi $cm$^{2}$ of red paint. Find the radius of this bowl.

Surface Area and Volume of Hemispheres

<p>A spherical ball bearing has a volume of $0.538$ cm$^{3}$. Find</p>
<ol class="i-list"><li><div class="list-item-paragraph">its radius,</div></li><li><div class="list-item-paragraph">the mass of $2500$ identical ball bearings if they are made of aluminium of density $2.73$g/cm$^{3}$.<br></div></li></ol>

A spherical ball bearing has a volume of $0.538$ cm$^{3}$. Find

Spherical Ball Bearing: Radius and Mass Calculation

<p>A spherical marble ball has a radius of $1.35$ cm.</p>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the volume,</div></li><li><div class="list-item-paragraph">the surface area,</div></li></ol>
<p>of the marble ball.</p>

A spherical marble ball has a radius of $1.35$ cm.

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