Question

a dart is thrown and land in the interior of the circle what is the probability that the Dart will land in the shaded region​

Answer 1

Answer:

We have

AB = CD = 8 and AD = BC = 6

using Pythagoras Theorem is ? ABC, we have

AC2 = AB2 + BC2

AC2 = 82 + 62 = 100

AC = 10

OA = OC = 5 [ Q O is the midpoint of AC]

∴ Area of the circle = π (OA)2 = 25 π sq units [Q Area = π r2]

Area of rectangle ABCD = AB x BC = 8 x 6 = 48 sq units

Area of shaded region = Area of the circle - Area of rectangle ABCD Area of shaded region = 25 π - 48 sq unit.

Hence P (Dart lands in the shaded region) = Area of shaded region/Area of circle = 25π - 48/25π

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Answer 2

Answer

61/157

Explanation

A dart is thrown and lands in the interior of the circle.

Probability that it will land in the shaded region = area of shaded region/area of circle

We will need to find the radius of circle.

Clearly, diagonal of the rectangle = diameter of the circle.

By Pythagoras theorem, we can calculate diagonal of the rectangle

→ diagonal = 10 units

Now, this means

diameter = 10 units

→ radius = 5 units

So, area of circle = πr² = (5)²π sq. units. = 25π sq. units

And, area of shaded region = area of circle - area of rectangle

area of rectangle = l × b = 6 × 8 = 48 sq. units

So area of shaded region = 25π - 48

Taking π as 3.14, we get

25(3.14) - 48 = 78.5 - 48 = 30.5 sq. units

So , probability = 30.5/78.5 = 61/157