Question

A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a dice, very small in size, is dropped on the rectangular paper without seeing towards it. If the dice falls and lands on the paper only, find the probability that it will fall and land inside the circle. 

Answer 1

Diameter of the circle = 20 cm

Radius = 10 cm 

Area of circle = πr²

= `22/7 xx 10 xx 10`

= `2200/7 cm^2` 

Length of paper = 40 cm 

Width of paper = 30 cm 

Area of paper = 1200 cm² 

Total possible outcomes = area of rectangular paper 

Since paper is kept on table top and dice falls and land on paper.

Number of favorable outcomes = area of circle.

P(inside the circle) = `"Area of circle"/"Area of rectangular paper"`

= `(2200/7)/1200`

= `11/42`