What is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot?

Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 19 feet. Container B has a diameter of 26 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

After the pumping is complete, what is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot?

Answer 1

volume = height times pi times radius squared

volume = hpi(d/2)^2 = hpi(r^2)

if h=19, d=16 then r=d/2 = 8

volume of Container A is 19(pi)(8^2) = 1216pi ft^3

if h=13, d= 26, then r= d/2 = 13 and

volume of Container B is 13pi(13^2) = 2197pi ft^3

difference in volumes = 2197pi - 1216pi = 981pi ft^3 = the empty portion of Container B

981pi = about 981(3.14159) = about 3081.89979 =3081.9 ft^3 rounded off to decimal place

= empty portion of Container B

308.9 ft^3 to the nearest tenth of a cubic foot

Answer 2

Hi Roman J.

Calculate the volume of both cylinders, then subtract the volume of the smaller cylinder from the larger cylinder.

Volume of a cylinder is πr²h

I hope this helps.