Question

The volume of an object is equal to the ratio of its mass to density, V = StartFraction m Over d EndFraction. The mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter.

What is the radius of the grape? Round to the nearest tenth of a centimeter.

Answer 1

First find the volume: V = m/d = 8.4/2 = 4.2 cm^3.

For a sphere, V = (4/3)πr^3, so
r = [3V/(4π)]^(1/3) = [3(4.2)/(4π)]^(1/3).

Compute:
r ≈ [12.6/(4π)]^(1/3) = [3.15/π]^(1/3) ≈ 1.0009 cm.

Rounded to the nearest tenth: 1.0 cm.