Question

Question 20 of 33

What is the surface area of the sphere shown below with a radius of 7?
1.72
A. 495 sq. units
B. 65x sq, units
C. 457 sq. units
D. 1965 sq. units
SERNAT

Answer 1

The surface area of the sphere 1s 615.75 sq. unit.

Explanation:

The surface area of a sphere
`A_s` = 4·π·r²

Given that the radius of the sphere = 7, we have

The surface area of the sphere = 4 × π × 7^2 = 615.75 sq. unit

The surface area can also be derived from the volume of the sphere by differentiation as follows;

Volume of a sphere, V = 4/3·π·r³

(The volume of the sphere is 4/3·π·7³ = 1436.76 cube unit)

dV/dr = d(4/3·π·r³)/dr = 3×4/3·π·r² = 4·π·r²

The surface area of the sphere = 615.75 sq. unit.