FIND THE AREA OF A CIRCLE

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.

Problem 10 :

The Hillsboro Inlet Lighthouse lights up how much more area than the Jupiter Inlet Lighthouse?

Solution :

Area of jupiter inlet light house = πr²

Here r = 18 ft

= π(18)²

= 324 π square miles.

Area of Hillsboro inlet light house = πr²

Here r = 28 ft

= π(28)²

= 784 π square miles.

Difference between area = 784 π - 324 π

= 460π

So, Hillsboro inlet light house's are is 460π is greter than jupiter inlet light house.

Problem 11 :

A dog is leashed to the corner of a house. How much running area does the dog have? Explain how you found your answer.

Solution :

Area of circle = πr²

Here r = 20 ft

= π(20)²

= 400 (3.14)

= 1256 square feet

So, the running area of the dog it 1256 square feet.

Problem 12 :

Is the area of a semicircle with a diameter of x greater than, less than, or equal to the area of a circle with a diameter of (1/2) x ? Explain.

Solution :

Area of semicircle = (1/2) x πr²

Diameter = x

radius = x/2

= (1/2) x π(x/2)²

= πx²/8

Area of circle = πr²

radius = (x/2)/2

= x/4

= π(x/4)²

= πx²/16

= (1/2) (πx²/8)

(1/2) Area of circle = area of semicircle

Area of circle = 2 (area of semicircle)

So, area of semicircle is lesser than area of circle.

Problem 13 :

The heart-shaped card is made up of a square and two semicircles. What is the area of the card?

Solution :

Area of the card = 2(area of semicircles) + area of square

= 2(1/2) πr² + side²

= 3.14 (4)² + 8²

= 3.14(16) + 64

= 50.24 + 64

= 114.24 cm²

So, area of the card is 114.24 cm².

Problem 14 :

A desktop is shaped like a semicircle with a diameter of 28 inches. What is the area of the desktop?

Solution :

Radius = 28/2

= 14 inches

Area of the desktop = πr²

= 3.14(14)²

= 3.14(196)

= 615.44 square inches.