Question

At the Kerry Hotel Pudong in Shanghai, China, theonce swimming pool is now the world's largest ballpit. The ball pit is 82 feet long and 41 feet wide,with an average depth of 4.25 feet. Each ball in the ball pit is the same size. They each have a diameterof 4 inches. 1. What is the volume of this pool? 2. How many ball pit balls will we need to fill the pool up to the top?

Answer 1

Answer: We have to find the volume of the pool and the number of pit balls that can fill it.

(1) We can find the volume of the pool with the following formula:

`V=L* W* D\rightarrow(1)`

Using the equation (1) the volume of the pool is determined as follows:

`\begin{gathered} L=82ft \\ \\ W=41ft \\ \\ D=4.25ft \\ \\ \therefore\rightarrow \\ \\ \begin{equation*} V=L* W* D \end{equation*} \\ \\ V=(82ft)*(41ft)*(4.25ft)=14,288.5ft^3 \\ \\ V=14,288.5ft^3 \end{gathered}`

(2) The number of ball pits that can fill the pool is as follows:

`\begin{gathered} V_b=(4)/(3)\pi r^3 \\ \\ \\ 4in=(1)/(3) \\ \\ \therefore\rightarrow \\ \\ V_b=(4)/(3)\pi((1)/(3))^3=(4)/(81)\pi ft^3 \\ \\ V_b=(4)/(81)\pi ft^3=0.16ft^3 \end{gathered}`

Therefore the answer is:

`\begin{gathered} N=(V)/(V_b)=(14,288.5ft^3)/(0.16ft^3)=89,303.125 \\ \\ N=89,303.125 \end{gathered}`