Chapter 7.2, Problem 60PPS

(a)

To determine

To find: The ratio of the area of the circle to the area of the square.

Answer to Problem 60PPS

The ratio of the area of the circle to the area of the square $=\frac{\pi }{4}$ .

Explanation of Solution

Given information:

Given, the area of a circle $A=\pi r^2$ and the area of a square is $A=s^2.$

Calculation:

Calculate the expression

The length of one side of the square is equal to the diameter of the circle $s=2r.$

Then

  $\begin{array}{c}\frac{Circle}{Square}=\frac{\pi r^2}{{\left(2r\right)}^2}\\ =\frac{\pi r^2}{4r^2}\\ =\frac{\pi }{4}{r}^{2-2}\\ =\frac{\pi }{4}{r}^0\\ =\frac{\pi }{4}\end{array}$

Therefore, the solution of the expression is $=\frac{\pi }{4}$ .

(b)

To determine

To find: the ratio of the area of the circle to the square.

Answer to Problem 60PPS

Replace $r$ with $2r$ in the equations: $s=2\cdot 2r=4r$ .

Explanation of Solution

Given information:

Given, the area of a circle $A=\pi r^2$ and the area of a square is $A=s^2.$

Calculation:

Calculate the expression

Replace $r$ with $2r$ in the equations: $s=2\cdot 2r=4r$ .

Therefore the solution of the equation is above.

(c)

To determine

To find: copy and complete the table.

Answer to Problem 60PPS

Table is completed in calculation.

Explanation of Solution

Given information:

Given, the area of a circle $A=\pi r^2$ and the area of a square is $A=s^2.$

Calculation:

Calculate the expression

  $$

Therefore the solution of the equation is above.

(d)

To determine

To find: The ratio of the area of the circle to the area of the square

Answer to Problem 60PPS

The ratio of the area of the circle to the area of the square $=\frac{\pi }{4}.$

Explanation of Solution

Given information:

Given, the area of a circle $A=\pi r^2$ and the area of a square is $A=s^2.$

Calculation:

Calculate the expression

The ratio of the area of the circle to the area of the square will always be $\frac{\pi }{4}.$

Therefore the solution of the equation is above.