A, B and C are three spheres - Edexcel - GCSE Maths - Question 20 - 2021 - Paper 2

For sphere B:

$27 = \frac{4}{3} \pi r_B^3$

Rearranging gives:

$r_B^3 = \frac{27 \times 3}{4 \pi}$

Evaluating this yields:

$r_B^3 \approx 6.43$

Thus,

$r_B = \sqrt[3]{6.43} \approx 1.86 \text{ cm}$

Using the ratio of the radii, where the ratio of radius of sphere B to radius of sphere C is 1:2, we get:

$r_C = 2r_B$

So,

$r_C = 2 \times 1.86 \approx 3.72 \text{ cm}$

The surface area of a sphere is given by the formula: $SA = 4 \pi r^2$

For sphere A:

$SA_A = 4 \pi (3.07)^2 \approx 118.70 \text{ cm}^2$

For sphere C:

$SA_C = 4 \pi (3.72)^2 \approx 174.90 \text{ cm}^2$

Now we find the ratio of the surface areas:

$\text{Ratio} = \frac{SA_A}{SA_C} = \frac{118.70}{174.90} \approx 0.678 \approx 1:1.47$