Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 6 feet and a height of feet. Container B has a diameter of 4 feet and a height of feetContainer 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 water in Container B, to the nearest tenth of a cubic foot ?

Answer 1

ANSWER

$84.8ft^3$

EXPLANATION

First, we have to find the volume of both containers.

The volume of a cylinder is given as:

$V=\pi\cdot r^2\cdot h$

where r = radius; h = height

The diameters of both containers are given instead of their radii.

Radius is half of the diameter, this means that:

$\begin{gathered} r_A=3ft \\ r_B=2ft \end{gathered}$

Therefore, the volume of container A is:

$\begin{gathered} V=\pi\cdot3^2\cdot3 \\ V=84.8ft^3 \end{gathered}$

And the volume of container B is:

$\begin{gathered} V=\pi\cdot2^2\cdot7 \\ V=88.0ft^3 \end{gathered}$

As we can see, the volume of container A is less than the volume of container B.

This means that after the water is pumped completely out of container A into container B, the volume of water in container B is equal to the volume of container A (since container A was filled with water).

Therefore, the volume of water in container B after pumping is:

$84.8ft^3$