Chapter 10.4, Problem 8C

To determine

To calculate the diameter when given its area different.

Answer to Problem 8C

  $d=2\sqrt{\frac{A}{\pi }}$

Explanation of Solution

Given Information: Area and Radius

Formula Used:Area of circle = $\pi \times r^2$ , $\pi =\frac{22}{7}$ , $diameter=2\times radius$

Calculation:

Area = A, Diameter = d, Radius = r.

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

Multiply and Divide the Area of Circle by 4.

Area of circle = $\frac{1}{4}\times \pi \times 4\times r^2$

So,

A = $\frac{1}{4}\times \pi \times (4\times r^2)$

So,

A = $\frac{1}{4}\times \pi \times {(2r)}^2$

  $diameter=2\times radius$

A = $\frac{1}{4}\times \pi \times {(d)}^2$

Hence,

  ${(d)}^2=\frac{4\times A}{\pi }$

Square root of d.

  $d=\sqrt{\frac{4\times A}{\pi }}$

Hence,

  $d=2\sqrt{\frac{A}{\pi }}$