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

  B)  108π cm^2

Step-by-step 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.

B) 108π cm2

Step-by-step 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