CPM Homework Help : A2C Problem 4-70

Lilia wants to have a circular pool put in her backyard. She wants the rest of the yard to be paved with concrete.

If her yard is a $50$ ft. by $30$ ft. rectangle, what is the largest radius pool that can fit in her yard?
Step 1 (a):
Draw the rectangle.
Step 2 (a):
Fit the largest possible circle into the rectangle (it does not have to be in the center).
Answer (a):
The radius of the pool is $15$ ft.
If the concrete is to be 8 inches thick, and costs $$2.39$ per cubic foot, what is the cost of putting in the concrete? No concrete will be used in the pool. (Reminder: Volume = (Base Area · Depth ).

Step 1 (b):

Find the area of the yard (rectangle) and the area of the pool (circle).

Step 2 (b):

Subtract the area of the pool from the area of the yard to find the area that will be paved.

A = 1500 − 225π ≈ 793.14 ft.²

Step 3 (b):

$\text{Since 8 inches is } \frac{2}{3} \text{of a foot, multiply the area of the region to be paved by two thirds.}$

$V = 793.14 \cdot \frac{2}{3} \approx 528.76 \text{ ft.}^{3}$

Step 4 (b):

Now multiply by the price per cubic foot to find the total cost.

$C=528.76 \text{ ft.}^{3} \cdot 2.39 \frac{\text{dollars}}{\text{ft.}^{3}}$

Answer (b):

The total cost is $$1,263.74$ .