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PSLE

<p>The figure below shows a staircase-shaped prism of a uniform cross section. Given that every step is identical and is $30$ cm in breadth, $400$ cm in length and $40$ cm in height, find</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/1767771330133-k7exdvpby0k.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzEzMzAxMzMtazdleGR2cGJ5MGsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjczMiwiZXhwIjoxNzkyNjYzMDMyfQ.hIp9mLhmWCKSKVrzLq1w4FLaCAR1wBbASPOVzubsnUk" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-1767771333313-g1qo5jp1j" data-list-item-path="item-1767771333313-g1qo5jp1j"><div class="list-item-paragraph">the area of the cross section in $\text{m}^2$,</div></li><li data-list-item-id="item-1767771333897-jrgt8arj2" data-list-item-path="item-1767771333897-jrgt8arj2"><div class="list-item-paragraph">the total surface area of the prism in $\text{m}^2$, and</div></li><li data-list-item-id="item-1767771334921-8yysn2035" data-list-item-path="item-1767771334921-8yysn2035"><div class="list-item-paragraph">the volume of the prism in $m^3$.</div></li></ol>

The figure below shows a staircase-shaped prism of a uniform cross section. Given that every step is identical and is $30$ cm in breadth, $400$ cm in length and $40$ cm in height, find

Conversion between Cubic Units

Volume and Surface Area of Composite Solids

Conversions between Square Units

Volume and Surface Area of Prisms

Perimeter and Area of Plane Figures

<p>The figure below shows a solid that is the remaining part of a larger triangular prism with a smaller triangular prism carved out of it.</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/1767770715447-jfu9gqyq22n.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc3NzA3MTU0NDctamZ1OWdxeXEyMm4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjczMiwiZXhwIjoxNzkyNjYzMDMyfQ.nn2Elza5p4A1vHo5eo9hewIoLLRsAcsIuwkocfLySP8" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the area of the cross section in <strong>cm²</strong>.</div></li><li><div class="list-item-paragraph">the total surface area of the solid in <strong>cm²</strong>.</div></li><li><div class="list-item-paragraph">the volume of the solid in <strong>cm³</strong>, </div></li></ol>
<p>correcting your answers to the nearest integer.</p>

The figure below shows a solid that is the remaining part of a larger triangular prism with a smaller triangular prism carved out of it.

correcting your answers to the nearest integer.

<p>The figure below shows a solid of a uniform cross section, where the circular portion is a quadrant, and an isosceles right-angled triangular prism is removed from the solid. Find, correcting your answers to the nearest integer,</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/1767694543950-zsch4vo2if.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTQ1NDM5NTAtenNjaDR2bzJpZi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzMyLCJleHAiOjE3OTI2NjMwMzJ9.qEGqrth5kwSjfYrNxuDrDGQF7ARDmxaDCm4f1T04OE4" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">the area of the cross section in cm$^2$,</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">the total surface area of the solid in cm$^2$, and</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">the volume of the solid in cm$^3$.</div></li></ol>
<p>The source labels the sloping cut as 240 mm. This is rounded: its two perpendicular sides are 170 mm, so the exact sloping length is $170\sqrt2\text{ mm}$. Use the exact sloping length before rounding the requested answers.</p>

The figure below shows a solid of a uniform cross section, where the circular portion is a quadrant, and an isosceles right-angled triangular prism is removed from the solid. Find, correcting your answers to the nearest integer,

the area of the cross section in cm$^2$,

the total surface area of the solid in cm$^2$, and

The source labels the sloping cut as 240 mm. This is rounded: its two perpendicular sides are 170 mm, so the exact sloping length is $170\sqrt2\text{ mm}$. Use the exact sloping length before rounding the requested answers.

<p>The figure below shows a pentagonal prism. Given that the perimeter of its cross section is $489.4$mm, find, correcting your answers to the nearest integer,</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/1767694189025-w6omtkdpz0o.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2OTQxODkwMjUtdzZvbXRrZHB6MG8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2MjczMiwiZXhwIjoxNzkyNjYzMDMyfQ.EG09hQ8ClaWM2STKnVnJfLS0IZ0qckxtyKupt9lgeQk" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the value of $x$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the area of the cross section in cm$^2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total surface area of the prism in cm$^2$, and</span></div></li><li><div class="list-item-content"><span class="list-item-text">the volume of the prism in cm$^3$.</span></div></li></ol>

The figure below shows a pentagonal prism. Given that the perimeter of its cross section is $489.4$mm, find, correcting your answers to the nearest integer,

the total surface area of the prism in cm$^2$, and

<p>Express</p>
<ol class="i-list"><li><div class="list-item-paragraph"><strong>$170\ 964$cm$^3$ in m$^3$</strong></div></li><li><div class="list-item-paragraph"><strong>$7.97$m$^3$ in litres</strong></div></li><li><div class="list-item-paragraph"><strong>$2\ 481$millilitres in m$^3$</strong></div></li><li><div class="list-item-paragraph"><strong>$729$litres in cm$^3$</strong></div></li></ol>

<p>Express</p>
<ol class="i-list"><li><div class="list-item-paragraph">$2.5$m$^3$ in cm$^3$</div></li><li><div class="list-item-paragraph">$0.00029$m$^3$ in cm$^3$</div></li><li><div class="list-item-paragraph">$0.94$m$^3$ in millilitres</div></li><li><div class="list-item-paragraph">$6.32$litres in millilitres</div></li></ol>

<p>Find the ratio of</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$0.7\text{h}$ to $56 \text{ min}$ to $3960\text{s}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$1\frac{1}{4} \text{m}$ to $205\text{cm}$ to $1750\text{mm}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$500\mathrm{g}$ to $10.25\text{kg}$ to $0.04\text{tonnes}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$250\text{ml}$ to $7.50\text{litre}$ to $1500\text{ml}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\$27.20$ to $\$6.80$ to $40\text{¢}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{1}{125} \text{m}^{3}$ to $4\text{dm}^{3}$ to $7000\text{cm}^{3}$</span></div></li></ol>

$0.7\text{h}$ to $56 \text{ min}$ to $3960\text{s}$

$1\frac{1}{4} \text{m}$ to $205\text{cm}$ to $1750\text{mm}$

$500\mathrm{g}$ to $10.25\text{kg}$ to $0.04\text{tonnes}$

$250\text{ml}$ to $7.50\text{litre}$ to $1500\text{ml}$

$\frac{1}{125} \text{m}^{3}$ to $4\text{dm}^{3}$ to $7000\text{cm}^{3}$

Simplifying Ratios

 Ratio

Ratio, Rate and Speed

<p>Express $28000 \mathrm{ \, m}l$ as a percentage of $7$ m${^3}$.</p>

Express $28000 \mathrm{ \, m}l$ as a percentage of $7$ m${^3}$.

Expressing One Quantity as a Percentage of Another

Volume Percentage Conversion

Percentages

<p>Convert</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$0.486$ m${^3}$ to cm${^3}$,</div></li><li><div class="list-item-paragraph">$1750$ cm${^3}$ to m${^3}$,</div></li><li><div class="list-item-paragraph">$2.33$ litres to cubic centimetres.</div></li></ol>

Volume Conversion Practice

<p>Express</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$0.67$ m${^3}$ in millilitres,</div></li><li><div class="list-item-paragraph">$2940$ millilitres in litres,</div></li><li><div class="list-item-paragraph">$30.6$ litres to cm${^3}$.</div></li></ol>

Metric Volume Unit Conversions

<p>Express</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$234000$ cm${^3}$ in m${^3}$,</div></li><li><div class="list-item-paragraph">$5$ m${^3}$ to cm${^3}$,</div></li><li><div class="list-item-paragraph">$0.0491$ m${^3}$ to millilitres.</div></li></ol>

Expressing Volumes in Different Units

<p>Express $120$ cm${^3}$ as a percentage of $6.8$ litres.</p>

Express $120$ cm${^3}$ as a percentage of $6.8$ litres.

Percentage involving Volume

<p>Express</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$1.5$ m${^3}$ in cm${^3}$,</div></li><li><div class="list-item-paragraph">$3.2$ cm${^3}$ in m${^3}$,</div></li><li><div class="list-item-paragraph">$2.3$ m${^3}$ in millilitres.</div></li></ol>

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