Question

From a circular sheet of paper with radius $20$ cm, $4$ circles of radius $5$ cm each are cut out. Find the ratio of the uncut to the cut portions.

• A. $1:3$
• B. $4:1$
• C. $3:1$
• D. $4:3$

Answer 1

Answer: (C)

$3:1$

Area of large circular sheet $=\pi R^2=\pi \times {20}^2=400\pi {cm}^2$

Area of circles $=4\times \pi r^2=4\pi \times {\left(5\right)}^2=100\pi {cm}^2$

Area of uncut portion $=400\pi -100\pi =300\pi {cm}^2$

Required ratio $=300\pi :100\pi =3:1$