Question

ASAPPPPPP 100 POINTS GUYS CMON LAST HW QUESTION

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 6 feet and a height of 9 feet. Container B has a radius of 5 feet and a height of 12 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 full after the pumping is complete?

Answer 1

The nearest tenth, Container A is about 46.3% full after the pumping is complete.

Explanation:

To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.

The volume of water in Container A can be found using the formula for the volume of a cylinder:

V_A = πr^2h = π(6^2)(9) = 324π cubic feet

The volume of Container B can also be found using the same formula:

V_B = πr^2h = π(5^2)(12) = 300π cubic feet

After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:

V_A' = πr^2h' = 300π

h' = 300/(36π) = 25/6 feet

So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:

(25/6) / 9 * 100% ≈ 46.3%

Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.