Question

C С
4. In the given figure,
ABCD is a rectangle and
D
8 units
O is the centre of circle. If
a dart is thrown and lands
6 units
in the interior of the circle,
then what is the probability A
that the dart will land in
the shaded region?
0
В B.​

Answer 1

Explanation:

Chapter 16. Probability

16. Probability, Question NO.4706

Question

In Fig., a dart is thrown and lands in the interior of the circle. What is the probability that the dart will land in the shaded region?

Answer

Using Pythagoras theorem in \triangleABC, we have

AC2 = AB2 + BC2

\Rightarrow AC2 = 82 + 62 = 100

\Rightarrow AC = 10

\Rightarrow OA = OC = 5 [\because O is the mid-point of AC]

Area of the circle = \pi (OA)2 = 25\pisq. units [Area = \pir2]

Area of rectangle \triangleBCD = AB \times BC = 8 \times 6 = 48 sq. units

Area of shaded region = Area of the circle - Area of rectangle ABCD

\Rightarrow Area of shaded region = 25 \pi - 48 sq. units

Hence, P (dart lands in the shaded region) = \frac{\text { Area of shaded region }}{\text { Area of circle }}=\frac{25 \pi-48}{25 \pi}