Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 24 feet and a height of 15 feet. Container B has a diameter of 18 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.

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

Answer 1

To calculate the percent of Container A that is empty after the pumping is complete, we need to calculate the volume of water in Container B and compare it to the volume of Container A.

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height.

Container A:

Diameter = 24 feet

Radius = Diameter / 2 = 24 / 2 = 12 feet

Height = 15 feet

Container B:

Diameter = 18 feet

Radius = Diameter / 2 = 18 / 2 = 9 feet

Height = 19 feet

Now let's calculate the volumes:

Volume of Container A = π * (12^2) * 15 ≈ 6785.4 cubic feet

Volume of Container B = π * (9^2) * 19 ≈ 4848.5 cubic feet

To find the percent of Container A that is empty, we can calculate the ratio of the empty space to the total volume:

Empty space in Container A = Volume of Container A - Volume of Container B

= 6785.4 - 4848.5

= 1936.9 cubic feet

Percent of Container A that is empty = (Empty space / Volume of Container A) * 100

= (1936.9 / 6785.4) * 100

≈ 28.5%

Therefore, to the nearest tenth, approximately 28.5% of Container A is empty after the pumping is complete.