Question

A target is shown in fig. below consists of three concentric circles of radii, 3, 7 and 9 cm respectively. A dart is thrown and lands on the target. What is the probability that the dart will land on the shaded region?

Answer 1

We have,

1^st circle – with radius 3

2^nd circle – with radius 7

3^rd circle – with radius 9

So, their areas would be

Area of 1^st circle = π(3)² = 9π

Area of 2^nd circle = π(7)² = 49π

Area of 3rd circle = π(9)² = 81π

Area of shaded region = Area of 2^nd circle – Area of 1^st circle

= 49π − 9π

= 40π

Probability that it will land on the shaded region

Therefore, the probability that the dart will land on the shaded region is \(\frac{40}{81}\).