Question

Find the surface area of a sphere with a great circle that has an area of 49 π square miles.

A. 225π mi2
B. 196 π mi2
C. 126 π mi2
D. 343 π mi2

Answer 1

The answer is B. 196 π mi2

(1) Find radius r:
The area of the circle is:
A = r²π
A = 49π mi²

49π = r²π
49 = r²
r = √49 = 7 mi

(2) Find the surface area of the sphere.
The surface area of the sphere is:
A = 4πr²
r = 7 mi
A = 4π * 7²
A = 4π * 49
A = 196π mi²