Chapter 11.8, Problem 34HP

To determine

To compute the area of circle B.

Answer to Problem 34HP

  $50$ square yards.

Explanation of Solution

Given information: Area of the circle A$=8$ square yards.

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

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

Calculation: $a=\pi \times r^2$

Changing the equation to compute radius ‘r’.

  $r^2=\frac{a}{\pi }$

This can be simplified to

  $r=\sqrt{\frac{a}{\pi }}$

  $=\sqrt{\frac{50\times 7}{22}}$

Taken ‘pi’ as $\frac{22}{7}$

  $=\sqrt{\frac{56}{22}}$

Now, radius of circle B can be shown as 2.5 times the radius of circle A.

  $R=2.5\times \sqrt{\frac{56}{22}}$

This can be used in the formula to compute the area of the area B.

Hence,

  $B=\pi \times R^2$

Formula for area of circle B.

  $=\frac{22}{7}\times {\left(2.5\times \sqrt{\frac{56}{22}}\right)}^2$

Putting the value of the radius.

  $=\frac{22}{7}\times \left(6.25\times \frac{56}{22}\right)$

Expanding the expression.

  $=6.25\times 8$

On multiplying this

  $=50$ square yards.