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The diagram shows a prism - Edexcel - GCSE Maths - Question 7 - 2021 - Paper 1

Question 7

The diagram shows a prism. The cross section of the prism is a right-angled triangle. The base of the triangle has length 5 cm. The prism has length 25 cm. The pris... show full transcript

Worked Solution & Example Answer:The diagram shows a prism - Edexcel - GCSE Maths - Question 7 - 2021 - Paper 1

Step 1

Work out the area of the cross section

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Answer

The volume of a prism is given by the formula: $V = A \times h$ where:

$V$ is the volume
$A$ is the area of the cross section
$h$ is the height (or length) of the prism.

Given that the volume is 750 cm³ and the length of the prism is 25 cm, we can rearrange the formula to find the area of the cross section: $A = \frac{V}{h} = \frac{750}{25} = 30 \text{ cm}^2$

Step 2

Find the height of the triangular cross section

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Answer

The area of a right-angled triangle is also given by: $A = \frac{1}{2} \times \text{base} \times \text{height}$ In this case, the base is 5 cm. Thus, we can rearrange the formula to find the height ( $h$ ) of the triangle: $30 = \frac{1}{2} \times 5 \times h$ Multiplying both sides by 2 gives us: $60 = 5h$ Now, divide both sides by 5: $h = \frac{60}{5} = 12 \text{ cm}$

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