Shape S is one quarter of a solid sphere, centre O - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 2

The surface area of Shape S consists of two parts: the curved surface area and the flat circular base.

1. Curved Surface Area (CSA): The formula for the curved surface area of a hemisphere (which is what S represents) is:

   $CSA = 2\pi r^2$

   Plugging in the value of ( r ):

   $CSA = 2\pi (13.0)^2 \approx 2\pi (169) \approx 1065.4 \text{ cm}^2$

2. Base Area: The base area of the circle is given by:

   $A = \pi r^2 \approx \pi (13.0)^2 \approx 3.14 \cdot 169 \approx 530.8 \text{ cm}^2$

3. Total Surface Area (TSA): Combining both areas gives:

   $TSA = CSA + A \approx 1065.4 + 530.8 \approx 1596.2 \text{ cm}^2$

Finally, rounding the answer to 3 significant figures:

$TSA \approx 1590 \text{ cm}^2$