Question

Shape S below is exactly one quarter of a solid sphere, centre O.

The volume of shape S is 19447 cm
O
Find the surface area of S.
Give your answer correct to 3 significant figures.
You must show your working.
+
Shapes
Volume of sphere =
1 / 놓자
Surface area of sphere = 4ter?
Total marks: 5

Answer 1

2,040 cm²

Explanation:

Given:

Volume of quarter sphere = 1,944π cm³

Required:

Surface area

Solution:

✔️First, find the radius (r).

Volume of the quarter sphere = ¼(⁴/3πr³)

Thus:

1944π = ¼(⁴/3×π×r³)

1944π = ⅓×π×r³

Multiply both sides by 3

1944π×3 = 1×π×r³

5,832π = πr³

Divide both sides by π

5,832π/π = r³

5,832 = r³

Find the cube root of both sides

r = 18

Radius = 18 cm

✔️Find the surface area of the quarter sphere

Surface area of quarter sphere = ¼ of 4πr² + 2(½ of πr²)

Radius (r) = 18 cm

Plug in the values

Surface area of quarter sphere = ¼×4×π×18² + 2(½×π×18²)

= π×18² + π×18²

= 2,035.75204 ≈ 2,040 cm² (to 3 SF)