A circle with diameter 20 cm is drawn somewhere on a rectangular … - Vidyadip

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 die, very small in size, is dropped on the rectangular paper without seeing towards it. If the die falls and lands on paper only, find the probability that it will fall and land : outside the circle

✓

Answer

Diameter of the circle $= 20$
Radius $= 10\ cm$
Area of circle $=\pi r^2=\frac{22}{7} \times 10 \times=\frac{2200}{7} cm ^2$
Length of paper $= 40\ cm$
Width of paper $= 30\ cm$
Area of paper $=1200\ cm ^2$
Total possible outcomes $=$ area of rectangular paper
P(outside the circle) $= 1 - P$ (inside the circle)
$=1-\frac{11}{42}$
$ =\frac{31}{42}$

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