Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 16 feet and a height of 19 feet. Container B has a radius of 18 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?

Answer 1

16.6%

Explanation:

You want the fraction of container B, a cylinder with radius and height of 18 ft, that remains empty after the contents of container A are pumped into it. Container A is a cylinder with radius 16 ft and height 19 ft.

Volume

The volume of a cylinder is given by the formula ...

V = πr²h

Fraction

The fraction of container B that is full after container A is emptied into it is ...

Va/Vb = (π(16 ft)²(19 ft))/(π(18 ft²)(18 ft)) = (16²·19)/18³

The fraction of container B that is empty, is the difference between 1 and this amount:

V'b = 1 -(16²·19)/18³ ≈ 0.166 = 16.6%

About 16.6% of container B remains empty.

<95141404393>