Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has a diameter of 12 feet and a height of 7 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 full after the pumping is complete?

Answer 1

79.4%

Explanation:

the volume of a cylinder is as for any other regular 3D object

base area × height

the base area is for a cylinder a circle.

so, it is

pi×r² × height

the radius (r) is always half of the diameter.

so, volume of cylinder A is

Va = pi×(10/2)² × 8 = pi×25 × 8 = 200pi ft³

the volume of cylinder B is

Vb = pi×(12/2)² × 7 = pi×36 × 7 = 252pi ft³

therefore, in a volume of 252pi ft³ we have 200pi ft³ filled with water.

252pi = 100% filling

1% = 100%/100 = 252pi/100 = 2.52pi

how many % are 200pi ?

as many as times 1% fit into 200pi :

200pi/2.52pi = 200/2.52 = 79.36507937... ≈ 79.4%