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Here are two similar solid shapes - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 3

Question 14

Here are two similar solid shapes. A B surface area of shape A : surface area of shape B = 3 : 4 The volume of shape B is 10cm³. Work out the volume of shape A.... show full transcript

Worked Solution & Example Answer:Here are two similar solid shapes - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 3

Step 1

surface area of shape A : surface area of shape B = 3 : 4

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Answer

Given the ratios of surface areas, we can find the ratio of their corresponding linear dimensions. The ratio of linear dimensions is the square root of the ratio of their surface areas:

$\text{Ratio of linear dimensions} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$

This means that the scale factor for volumes is:

$\text{Scale factor for volumes} = \left(\frac{\sqrt{3}}{2}\right)^3 = \frac{3\sqrt{3}}{8}$

Step 2

The volume of shape B is 10cm³.

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Answer

Let the volume of shape A be denoted as V_A. Since the volumes are related by the cube of the scale factor, we can write:

$V_B = \frac{3\sqrt{3}}{8} \cdot V_A$

Substituting the volume of shape B:

$10 = \frac{3\sqrt{3}}{8} \cdot V_A$

To find V_A, we can rearrange the equation:

$V_A = \frac{10 \cdot 8}{3\sqrt{3}} = \frac{80}{3\sqrt{3}}$

Step 3

Give your answer correct to 3 significant figures.

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Answer

Now, we can calculate V_A:

$V_A \approx \frac{80}{3 \cdot 1.732} \approx \frac{80}{5.196} \approx 15.39 \text{ cm}^3$

Rounding this to 3 significant figures gives:

$V_A \approx 15.4 \text{ cm}^3$

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