Question 54

What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 15 cm and 8 cm?

Solution

Let the radius of the required circle = r

Given,

Area of the required circle is equal to the sum of the areas of two circles whose radii 15 cm and 8 cm.

$$=$$> $$\pi\ r^2=\pi\ \left(15\right)^2+\pi\ \left(8\right)^2$$

$$=$$> $$r^2=15^2+8^2$$

$$=$$> $$r^2=225+64$$

$$=$$> $$r^2=289$$

$$=$$> $$r=17 cm$$

$$\therefore\ $$Radius of required circle = 17 cm

Hence, the correct answer is Option D

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