What is Area of a Circle ?
Area of a Circle is the region covered or enclosed within its boundary. It is measured in square units.
The formula for area of a circle is
Area = πr²
(where r is the radius of a circle)
If the given diameter of a circle, then the radius is
Radius (r) = (Diameter)/2
Find the area of each circle in terms of π.
Problem 1 :
Solution :
The formula for area of a circle is
= πr²
Here (r) = 15 ft.
= 15 × 15 × π
= 225π ft²
So, the area of the given circle is about 225π ft².
Problem 2 :
Solution :
By observing the figure, Diameter(d) = 22 in
Radius (r) = (diameter)/ 2
= (22)/2
r = 11 in
Area of a circle = πr²
= 11× 11 × π
= 121π in²
So, the area of the given circle is about 121π in².
Problem 3 :
Solution :
Formula for area of circle is
= πr²
Here (r) = 9 yd
= 9 × 9 × π
= 81π yd²
So, the area of the given circle is about 81π yd².
Problem 4 :
Solution :
By observing the figure, Diameter(d) = 12 yd
Radius (r) = diameter/2
= (12)/2
r = 6 yd
Area of a circle = πr²
A = 6 × 6 × π
= 36π yd²
So, the area of the given circle is about 36π yd².
Problem 5 :
Solution :
Area of a circle = πr²
Here (r) = 3 in
= 3 × 3 × π
= 9π in²
So, the area of the given circle is about 9π in².
Problem 6 :
Solution :
Diameter (d) = 34 ft
Radius (r) = (diameter)/ 2
= (34)/2
= 17 ft
Area of a circle = πr²
= 17 × 17 × π
= 289π ft²
So, the area of the given circle is about 289π ft².
Problem 7 :
If the radius is 10 ft, what will be the area of the circle?
Solution:
Area of a circle = πr²
Here (r) = 10 ft
= 10 × 10 × π
= 100π ft²
So, the area of the circle is about 100π ft².
Problem 8 :
What is the area of a circle with a diameter of 16 in?
Solution:
Diameter (d) = 16 in
Radius (r) = diameter/2
= (16)/2
r = 8 in
Area of a circle = πr²
= 8 × 8 × π
= 64π in²
So, the area of the circle is about 64π in².
Problem 9 :
A cow is tethered with a rope 20 ft long. What is the maximum area the cow can graze? Express your answer in terms of π.
Solution :
Given that a cow is tethered with a rope 20 ft long.
Here radius is the length of the rope.
Radius (r) = 20 ft.
Area of a circle = πr²
= 20 × 20 × π
= 400π ft²
Thus, the maximum area the cow can graze is 400π ft².
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