Question

A circular pool measures 12 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be?

Answer 1

Step 1:

In this question, we are given the following:

A circular pool measures 12 feet across.

One cubic yard of concrete is to be used to create a circular border of uniform width around the pool.

If the border is to have a depth of 6 inches, how wide will the border be?

Step 2:

From the question, we can see that:

`6\text{ inches = 0. 5 feet}`

`1\text{ cubic yard = 3 ft x 3ft x 3ft = }27ft^3`
`\begin{gathered} \text{Let the radius of the pool = ( 6+x ) feet} \\ \text{Let the width of the concrete that is used to } \\ \text{create the circular border = 6 feet} \end{gathered}`
`\text{Let the depth of the border = 6 inches = }(6)/(12)=\text{ 0. 5 inches}`

Step 3:

`\begin{gathered} U\sin g\text{ } \\ \pi R^2h\text{ - }\pi r^2\text{ h = 27} \\ \pi(6+x)^2\text{ 0. 5 - }\pi(6)^2\text{ 0. 5 = 27} \\ \text{0. 5}\pi(x^2\text{ + 12x + 36 - 36 ) = 27} \\ 0.\text{ 5 }\pi(x^2\text{ + 12 x) = 27} \\ \text{Divide both sides by 0. 5 }\pi\text{ , we have that:} \end{gathered}`
`x^2\text{ + 12 x - (}\frac{27}{0.\text{ 5}\pi})=\text{ 0}`

Solving this, we have that:

CONCLUSION:

From the calculations above, we can see that the value of the x:

( which is the width of the border ) = 1. 293 feet

(correct to 3 decimal places)