Question

A student takes a rectangular piece of paper 30 cm long and 21 cm wide. Find the area of the biggest circle that can be cut out from the paper. Also find the area of the paper left after cutting out the circle `("Take"  π = 22/7)`.

Answer 1

Given: A rectangular piece of paper 30 cm long and 21 cm wide.

Step-wise calculation:

1. The largest circle that fits inside the rectangle has diameter equal to the shorter side = 21 cm.

Radius r = `21/2`

= 10.5 cm

2. Area of the circle = πr²

Using `π = 22/7 : r^2` 

= 10.5² 

= 110.25 

Area (circle) = `22/7 xx 110.25` 

= 22 × 15.75

= 346.5 cm²   ...(Which is `693/2` cm²)

3. Area of the rectangle

= Length × Width

= 30 × 21

= 630 cm²

4. Area of paper left

= Area (rectangle) – Area (circle) 

= 630 – 346.5

= 283.5 cm²   ...(Which is `567/2` cm²)

Area of the biggest circle = 346.5 cm² `(693/2 cm^2)`.

Area of the paper left after cutting out the circle = 283.5 cm² `(567/2 cm^2)`.