Question

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

• A. 1:3
• B. 4:1
• C. 3:1
• D. 4:3

Hint:

Use the area formula for circles to find the total areas and then subtract the cut areas to get the uncut portion.

Answer 1

The Correct Option is C

The area of the circular sheet is: \[ \text{Area of large circle} = \pi r^2 = \pi (20)^2 = 400\pi \, \text{cm}^2 \] The area of one small circle (cut portion) is: \[ \text{Area of one small circle} = \pi (5)^2 = 25\pi \, \text{cm}^2 \] Since there are 4 small circles, the total area cut out is: \[ \text{Total area cut} = 4 \times 25\pi = 100\pi \, \text{cm}^2 \] The uncut area is: \[ \text{Area uncut} = 400\pi - 100\pi = 300\pi \, \text{cm}^2 \] Thus, the ratio of uncut to cut portions is: \[ \frac{300\pi}{100\pi} = 3:1 \] Therefore, the answer is c. 3:1.