From a circular sheet of radius 20 cm, three circles of radius 6 cm each are cut off. What is the ratio of the area of uncut to the area of the cut portion?

Correct option is D

Given:

Radius of large circular sheet = 20 cm

3 small circles of radius 6 cm each are cut

Find the ratio of uncut area to cut area

Formula Used:
Area of a circle = $$\pi r^2$$​​

Solution:

Uncut area =$$\pi(20)^2 - 3\pi(6)^2 = \pi(400 - 108) = 292 \pi$$​

Cut area =$$3\pi(6)^2 = 108\pi$$​

Required Ratio= $$\frac{\pi(292)}{\pi(108)} = \frac{292}{108}$$$$= \frac{73}{27}$$​​