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The diagram shows a prism - Edexcel - GCSE Maths - Question 10 - 2020 - Paper 3

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The diagram shows a prism. The cross section of the prism has exactly one line of symmetry. Work out the volume of the prism. Give your answer correct to 3 signifi... show full transcript

Worked Solution & Example Answer:The diagram shows a prism - Edexcel - GCSE Maths - Question 10 - 2020 - Paper 3

Step 1

Work out the height of the triangle

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Answer

To find the height of the triangular cross-section, we can use trigonometry. Given the angle at the top is 40°, the length of the base is 10 cm. We can use the sine function:

sin⁡(40∘)=height10\sin(40^\circ) = \frac{\text{height}}{10}

Rearranging gives:

height=10⋅sin⁡(40∘)\text{height} = 10 \cdot \sin(40^\circ)

Calculating this:

height≈10⋅0.6428≈6.428  cm\text{height} \approx 10 \cdot 0.6428 \approx 6.428 \; \text{cm}

Step 2

Calculate the area of the triangular cross-section

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Answer

Using the base and the height calculated earlier, the area, A, of the triangle can be calculated as:

A=12⋅base⋅height=12⋅10⋅6.428≈32.14  cm2A = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 10 \cdot 6.428 \approx 32.14 \; \text{cm}^2

Step 3

Find the volume of the prism

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Answer

The volume, V, of the prism can be calculated by multiplying the area of the cross-section by the length of the prism:

V=A⋅length=32.14⋅20≈642.8  cm3V = A \cdot \text{length} = 32.14 \cdot 20 \approx 642.8 \; \text{cm}^3

Rounding to 3 significant figures gives:

V≈643  cm3V \approx 643 \; \text{cm}^3

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