Chapter 3.2, Problem 54STP

To determine

Find the pool which is having the greatest are.

Answer to Problem 54STP

The circular shape pool is the greatest area as its radius is 9 ft.

Explanation of Solution

Given:

Three figures with dimensions:

  

Concept Used:

First figure is a rectangle. Area of rectangle is base times height

Area of rectangle: $\text{A}\text{=}\text{base}·\text{height}$

Second figure is a composite figure. A right angle with two half circle.

A = Area of rectangle + area of 2 half circle = Area of a rectangle + one full circle.

Total area of second figure: $\text{A}\text{=}\text{base}·\text{height}\text{+}\text{π}·{\text{(radius)}}^{\text{2}}$

Third figure is a circle. Area: $\text{A}\text{=}\text{π}·{\text{(radius)}}^{\text{2}}$

Calculation:

Let us calculate each area separately:

Area of rectangle: $\text{A}\text{=}\text{base}·\text{height}$ $\text{A}=12·18=216\text{sq}\text{ft}$ Area of the rectangular shape of the pool $216\text{sq}\text{ft}$

$\text{A}\text{=}\text{base}·\text{height}\text{+}\text{π}·{\text{(radius)}}^{\text{2}}$ Rectangle: base = 10 ft and height = 12 ft. Circle : radius = 6 ft $\begin{array}{l}\text{A}\text{=}\text{base}·\text{height}\text{+}\text{π}·{\text{(radius)}}^{\text{2}}\\ \text{A}\text{=}\text{10}·\text{12}\text{+}\text{3}\text{.14}·{\text{(6)}}^{\text{2}}\\ A=120+113.04=233.04\text{sq}\text{ft}\end{array}$

Area of circle: $\text{A}\text{=}\text{π}·{\text{(radius)}}^{\text{2}}$ ; radius = 9 ft $\text{A}\text{=}\text{3}\text{.14}·{\text{(9)}}^{\text{2}}=254.34\text{sq}\text{ft}$

The circular shape pool is the greatest area as its radius is 9 ft.

Thus, the circular shape pool is the greatest area as its radius is 9 ft.