Question

A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.

Answer 1

The largest area of the circle is possible when,

diameter = 42

Therefore, radius = `42/2` = 21 cm

Therefore, Area of circle = π × (21)²

= 1386

Area of the rectangle = 55 × 42 = 2310 cm² 

Therefore, area of remaining cardboard-

`= 42 xx 55 - pi (21)^2`

`= 42 xx 55 - 22/7 (21)^2`

= 2310 - 1386

= 924

Hence, the volume of the circle and area remaining cardboard-

= 1386 : 924

= 231 : 154

= 3 : 2