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Calculate the volume of the composite prism below in cubic metres. (2 marks)
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| \(\text{Area of cross-section }(A)\) | \(=\ \text{Rectangle 1 – Rectangle 2}\) |
| \(=(6\times 3)-(4\times 1)\) | |
| \(=18-4\) | |
| \(=14\ \text{m}^2\) |
| \(V\) | \(=A\times h\) |
| \(=14\times 11\) | |
| \(=154\ \text{m}^3\) |
Callum has designed a brick with two identical triangular sections removed as shown in the diagram below.
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| \(\text{Area of cross-section }(A)\) | \(=\ \text{Square – 2 × Triangle}\) |
| \(=(25\times 25)-2\times \Bigg(\dfrac{1}{2}\times 10\times 15\Bigg)\) | |
| \(=625-150\) | |
| \(=475\ \text{cm}^2\) |
| \(V\) | \(=A\times h\) |
| \(=475\times 40\) | |
| \(=19\ 000\ \text{cm}^3\) |
Calculate the volume of the prism below in cubic centimetres. (2 marks)
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| \(\text{Area of cross-section }(A)\) | \(=\ \text{Rectangle – Triangle}\) |
| \(=(16\times 10)-\Bigg(\dfrac{1}{2}\times 16\times 6\Bigg)\) | |
| \(=160-48\) | |
| \(=112\ \text{cm}^2\) |
| \(V\) | \(=A\times h\) |
| \(=112\times 8\) | |
| \(=896\ \text{cm}^3\) |
The composite prism below is made up of two right triangular prisms.
Calculate the volume of the composite prism in cubic metres. (2 marks)
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Calculate the volume of the composite prism below, giving your answer in cubic centimetres. (2 marks)
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\(\text{Convert measurements from mm to cm before calculations}\)
| \(\text{Area of cross-section }\) | \(=\ \text{Trapezium + Triangle}\) |
| \(=\Bigg(\dfrac{0.9}{2}\times(2.4+1.2)\Bigg)+\Bigg(\dfrac{1}{2}\times 2.4\times 1.5\Bigg)\) | |
| \(=1.62+1.8\) | |
| \(=3.42\ \text{cm}^2\) |
| \(V\) | \(=A\times h\) |
| \(=3.42\times 2.1\) | |
| \(=7.182\ \text{cm}^3\) |
Ben is designing blocks for a children's game. The block below is in the shape of a right prism and the dimensions are shown in the diagram.
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| \(\text{Area of cross-section }\) | \(=\ \text{Rectangle + Triangle}\) |
| \(=(8\times 6)+(\dfrac{1}{2}\times 6\times 4)\) | |
| \(=48+12\) | |
| \(=60\ \text{cm}^2\) |
| \(V\) | \(=A\times h\) |
| \(=60\times 7\) | |
| \(=420\ \text{cm}^3\) |
The local council builds a concrete bench in a public park. The bench is in the shape of a prism and the dimensions are shown in the diagram below.
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\(\text{Convert measurements from cm to m before calculations}\)
| \(\text{Area of cross-section }\) | \(=\ \text{Rectangle + Triangle}\) |
| \(=(0.6\times 0.75)+(\dfrac{1}{2}\times 0.3\times 0.3)\) | |
| \(=0.45+0.045\) | |
| \(=0.495\ \text{m}^2\) |
| \(V\) | \(=A\times h\) |
| \(=0.495\times 1.2\) | |
| \(=0.594\ \text{m}^3\) |