Shape S is one quarter of a solid sphere, centre O - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

The surface area of shape S consists of a quarter of the total surface area of a sphere and the base area (which is a circle):

1. Surface Area of the Sphere:

The total surface area ( A ) of a sphere is given by:

$A = 4 \pi r^2$

Substituting ( r \approx 5.173 ):

$A = 4 \pi (5.173)^2 \approx 4 \pi (26.83) \approx 4 \times 3.1416 \times 26.83 \approx 336.28 \text{ cm}^2$

Since shape S is one quarter of the sphere:

$A_{S1} = \frac{1}{4} \times 336.28 \approx 84.07 \text{ cm}^2$

2. Base Area (Circle):

The area of the circular base is:

$A_{base} = \pi r^2 \approx 3.1416 \times (5.173)^2 \approx 3.1416 \times 26.83 \approx 84.26 \text{ cm}^2$

3. Total Surface Area of S:

Adding the areas together gives:

$A_{total} = A_{S1} + A_{base} \approx 84.07 + 84.26 \approx 168.33 \text{ cm}^2$

Rounding this to three significant figures gives the final answer:

Answer: ( 168 \text{ cm}^2 )