Sunday, July 5, 2020
Sunday, June 21, 2020
Areas Related to Circles
12. Areas Related to Circles
Circle
The collection of points which is located at a certain distance from a certain point is said to be circle.
The certain distance is known as radius of the circle.
The certain point is known as centre of the circle.
The collection of points is known as circumference of the circle.
It is a geometrical figure in which infinite sides.
Area
The region which is surrounded by a closed geometrical figure is said to be area.
Calculation of area of a circle
When circle is divided into 16 equal parts from the centre of the circle. It is converted into a rectangle of length πr and breadth of r.
Important formulae of the circle
Area of cirle = πr²
Circumference of the circle = 2πr
Area of sector of a circle = πr²θ/360⁰
Area of minor segment = πr²2θ/360⁰ - r²sin2θ/2
Exercise 12.1
1. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Solution:
Let the radius of the circle be R.
We know that
Circumference of the circle = C = 2πr
From question it is clear that
r₁ = 19 cm
r₂ = 9 cm
R = ?
Therefore,
C = C₁ + C₂
Therefore,
R = 2π(r₁ + r₂)/2π
Therefore,
R = 19 + 9
R = 28 cm Ans.
2. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Solution
Let the radius be r.
From question it is clear that
r =?
r₁ = 8 cm
r₂ = 6 cm
Therefore,
Radius of the circle = r² = π(r₁² + r₂²)/π
r² = 8² + 6²
r² = 64 + 36
r² = 100
r = 10 cm. Ans.
Subscribe to:
Posts (Atom)