Area of a Circle Formula and Problems with Solutions
Circle – Area – Formula and Problems with Solutions
Area of a circle is A = 𝝿r2
= 𝝿 (pi) x (radius)2 , where r is radius of the circle.
or when we know the diameter A = (𝝿/4) x D2
when we know circumference A = c2/4𝝿
Let us now solve problems on area of a circle.
(1) The radius of a circle is 5 cm, what is the area of the circle.
Solution : Area of a circle is A = 𝝿r2
here radius of circle is 5 cm.
so, area of circle = 𝝿 x 52
= 3.14 x 5 x 5 cm2
Area of a circle is A = 78.5 cm2
(2) The radius of a circle is 30 cm, what is the area of the circle.
Solution : Area of a circle is A = 𝝿r2
here radius of circle is 30 cm.
so, area of circle = 𝝿 x 302
= 3.14 x 30 x 30 cm2
Area of a circle is A = 2826 cm2
(3) Diameter of a circle is 9.8 cm, what is the area of the circle.
Solution : Diameter of a circle is 9.8 cm
Therefore, radius of circle = 9.8/2 cm
= 4.9 cm
Area of a circle is A = 𝝿r2
here radius of circle is 4.9 cm.
so, area of circle = 𝝿 x (4.9)2
= 3.14 x 4.9 x 4.9 cm2
Area of a circle is A = 75.46 cm2
(4) In the figure two circles with same centre. The radius of larger circle is 8 cm, and radius of smaller circle is 4 cm.
(i)what is the area of the larger circle.
(ii)what is the area of the smaller circle.(iii)what is the area of the shaded part between two circles.
Solution : Area of a circle is A = 𝝿r2
here radius of larger circle is 8 cm.
so, area of larger circle = 𝝿 x 82
= 3.14 x 8 x 8 cm2 (i) Area of larger circle is = 200.96 cm2
now, radius of smaller circle is 4 cm.
so, area of smaller circle = 𝝿 x 42
= 3.14 x 4 x 4 cm2 (ii) Area of larger circle is = 50.24 cm2
(iii)The area of the shaded part between two circles
= 200.96 – 50.24 cm2
Area of shaded part = 150.72 cm2
(5) Find the perimeter of the given figure, which is a semicircle including its diameter.
Solution : Diameter of given semicircle = 14 cm(5)
so, radius = 14/2
= 7 cm
According to the question
perimeter of figure = circumference of semicircle + diameter
= 𝝿r + D
= 22/7 x 7 + 14
= 22 + 14
perimeter of figure = 36 cm