MATH SOLVE

3 months ago

Q:
# 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 cm2B) 108π cm2C) 180π cm2D) 432π cm2

Accepted Solution

A:

Answer: B) 108π cm^2Step-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 2πThe surface area of a hemisphere is 3 times the area of the circular face: S = 3πr^2 S = 3π(6 cm)^2 = 108π cm^2The surface area of the grapefruit half is 108π cm^2.