Question

What is the radius of a circle to the nearest cm whose area is equal to the sum of the areas of three circles of radii $22$ cm, $19$ cm and $8$cm respectively

• A. $17cm$
• B. $30cm$
• C. $29cm$
• D. $19cm$

Answer 1

Answer: (B)

$30cm$

Let the radius of such circle be $r$
We know that the area of a circle is given by $\pi \times radiu{s}^2$
Thus, $\pi r^2=\pi {22}^2+\pi {19}^2+\pi 8^2$
Cancelling $\pi$ on both sides
$r^2=484+361+64$ = $909$
$r=\sqrt{909}=30.15$
Thus, $r=30$ cm to the nearest cm.