Question

Two containers designed to hold water are side by side, both in the shape of acylinder. Container A has a diameter of 14 feet and a height of 17 feet. Container B hasa diameter of 18 feet and a height of 13 feet. Container A is full of water and the wateris 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 pumpingis complete?

Answer 1

79.1% of the Container B is full after the pumping.

Explanation:

The volume of a cylinder is represented as

`\begin{gathered} V=h\cdot\pi\cdot r^2 \\ \text{where,} \\ h=\text{ height} \\ r=\text{ radius} \end{gathered}`

Then, since the container has a diameter of 14 feet, which means a radius of 7 feet, and a height of 17 feet, its volume would be:

`\begin{gathered} V_A=17\cdot\pi\cdot7^2 \\ V_A=833\pi \end{gathered}`

Now, for container B, a radius of 9 feet and a height of 13 feet.

`\begin{gathered} V_B=13\cdot\pi\cdot9^2 \\ V_B=1053\pi \end{gathered}`

To determine the percent of container B after the pumping we can just make a simple cross multiplication, using proportional relation ships. Knowing that 1053pi is 100%, what would be 833pi from 1053pi

`\begin{gathered} \frac{1053\pi\text{ }}{833\pi}=(100)/(x) \\ 1053\pi\cdot x=100\cdot833\pi \\ x=(100\cdot833\pi)/(1053\pi) \\ x=79.1\text{ \%} \end{gathered}`