Answer:
2,040 cm²
Step-by-step 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)
