Chapter 11.9, Problem 29STP

To determine

To calculate the cost of cover of the pool.

Answer to Problem 29STP

G $\$824.74$ square feet.

Explanation of Solution

Given information:

Figure consists for a rectangle with length $l=18$ feet and breath $b=10$ feet.

It also consists of two equal semicircles with diameter $d=10$ feet or radius $r=\frac{d}{2}$

  $=\frac{10}{2}$

  $=5$ feet.

Formula used:

Area of rectangle $a=l\times b$ . Where ‘l’ is the length and ‘b’ is the breath.

Area of circle $a=\pi \times r^2$ where ‘r’ is the radius. Since both the semicircles are of equal diameter and radius.

For calculations, $\pi =3.14$ has been used.

Calculation: Calculate the area of the rectangle and circle. On adding the two, the area of the pool shall be derived.

  $a=l\times b$

Formula of rectangle

  $=18\times 10$

Multiply the length and breadth

  $=180$ square feet.

Next, calculate area of the circle.

  $a=\pi \times r^2$

Formula of circle

  $=3.14\times 5^2$

Expand the exponent of 5.

  $=3.14\times 25$

On simplification

  $=78.5$ square feet.

Adding the two areas $=a+c$ would give the area of the figure.

  $=180+78.5$

  $=258.5$ square feet.

Total cost of the cover

  $\$3.19$ per square meter

  $=\$3.19\times 258.5$

  $=\$824.615~\$824.74$