What is the volume of a hemisphere with a diameter of 59.5 ft, rounded to the nearest tenth of a cubic foot?

Answer 1

The formula for the volume of a sphere is V = (4/3)πr³

The problem provides the diameter, not the radius which is what we need to find the volume.

So the diameter is twice the radius, so we divide the diameter by 2 and find the radius.

r = 59.5/2 = 29.75 feet

The formula above is the volume of a WHOLE sphere, and we need the volume of HALF of a sphere, so we divide the Volume formula by 2.

Volume/2 = (4/6)πr³ which simplifies to

V(hemisphere) = (2/3)πr³

Plugging in r = 29.75 feet we get

V(hemisphere) = (2/3)π(29.75)³

Answer is: 55,146.7 cubic feet.