Question

Question - A grapefruit is approximately spherical. Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters. What is the surface area of one-half of the cut grapefruit?

A) 72π cm2
B) 108π cm2
C) 180π cm2
D) 432π cm2

Answer 1

B) 108π cm2

Explanation:

If a grapefruit is approximately spherical and Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters, the surface area of one-half of the cut grapefruit is 108π cm2.

Formula: 2πr

S = 3π(6 cm)^2

Answer 2

B) 108π cm^2

Explanation:

We assume the circumference measurement is the same as it would have been before the fruit was cut. In that case, the radius is found from ...

C = 2πr . . . . . . . . . formula relating circumference and radius

12π cm = 2πr . . . . substitute given information

6 cm = r . . . . . . divide by 2π

The surface area of a hemisphere is 3 times the area of the circular face:

S = 3πr^2

S = 3π(6 cm)^2 = 108π cm^2

The surface area of the grapefruit half is 108π cm^2.