A, B and C are three spheres - Edexcel - GCSE Maths - Question 1 - 2021 - Paper 3

The volume of sphere B is given as 27 cm³:

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

Rearranging gives:

$r_B^3 = \frac{27 \times 3}{4 \pi} \approx 6.43$

Calculating the radius:

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

Given the ratio of the radius of sphere B to that of sphere C is 1:2, we have:

$r_B : r_C = 1 : 2$

Thus:

$r_C = 2r_B = 2 imes 1.86 ext{ cm} \approx 3.72 ext{ cm}$

The surface area of a sphere is given by:

$SA = 4\pi r^2$

For sphere A:

$SA_A = 4\pi (3)^2 \approx 36\pi \text{ cm}^2$

For sphere C:

$SA_C = 4\pi (3.72)^2 \approx 4\pi (13.84) \approx 55.36\pi ext{ cm}^2$

Now, the ratio of the surface area of sphere A to C is:

$\frac{SA_A}{SA_C} = \frac{36\pi}{55.36\pi} \approx \frac{36}{55.36} \approx 0.65$

Thus, the ratio of the surface areas is approximately 36:55.36, which can be simplified to 9:13.