Chapter 11.9, Problem 33SR

To determine

To calculate the circumference and area of the circle.

Answer to Problem 33SR

Circumference $125.7$ inches and area $1257.1$ square inches.

Explanation of Solution

Given information:

Radius $r=20$ inches.

Formula used:

Circumference of circle $c=2\times \pi \times r$

Area of circle $a=\pi \times r^2$

Where ‘r’ is the radius of the circle.

For calculation, value of $\pi =\frac{22}{7}$ .

Calculation:

Circumference of circle

  $c=2\times \pi \times r$

Formula for circumference.

  $=2\times \frac{22}{7}\times 20$

Putting the value of radius ‘r’.

  $=\frac{880}{7}$

On simplifying the expression

  $=125.71$

Rounding the result to the nearest tenth.

  $=125.7$ inches.

Area of circle

  $a=\pi \times r^2$

Formula for area

  $=\frac{22}{7}\times {20}^2$

Putting the value of ‘r’ in the expression.

  $=\frac{22}{7}\times 400$

On further simplification

  $=\frac{8800}{7}$

On dividing the fraction

  $=1257.14$

Rounding the result to the nearest tenth.

  $=1257.1$ square inches.