FINDING THE AREA OF A CIRCLE

In this section, we are going to see the formula for area of a circle and also how the formula can be used to find area of a circle. 

The formula given below is used to find area of a circle. 

A  =  πr2

The area of a circle is equal to π times the radius squared. 

Question 1 :

Find the area of a circle whose radius is 7 cm.

Answer :

Step 1 : 

Area of a circle  =  πr²

Radius is given in the question. That is 7 cm. 

Substitute r  =  7  in the above formula. 

Area of the circle  =  π(7)²

Step 2 :

Since radius is a multiple of 7, we can use π  ≈  22/7.

Area of the circle  ≈  (22/7) x (7)²

Simplify

Area of the circle  ≈  22 x 7

Area of the circle  ≈  154 square cm. 

So, the area of the circle is about 154 square cm.

Question 2 :

Find the area of a circle whose diameter is 40 inches.

Answer :

Step 1 : 

Area of a circle  =  πr²

We know that

Radius  =  Diameter / 2

Radius  =  40/2  =  20 inches 

Step 2 :

Substitute r  =  20  in the above formula. 

Area of the circle  =  π(20)²

Step 3 :

Since radius is not a multiple of 7, we can use π  ≈  3.14.

Area of the circle  ≈  (3.14) x (20)²

Area of the circle  ≈  3.14 x 400

Area of the circle  ≈  1256 square in. 

So, the area of the circle is about 1256 square in.

Question 3 :

A biscuit recipe calls for the dough to be rolled out and circles to be cut from the dough. The biscuit cutter has a radius of 4 cm. Find the area of the top of the biscuit once it is cut. Use 3.14 for π.

Answer :

Since the top of the biscuit is in the shape of a circle, we can use area of circle formula to find area of the top of the biscuit.   

Step 1 : 

Area of a circle  =  πr²

Radius is given in the question. That is 4 cm. 

Substitute r  =  4  in the above formula. 

Area of the circle  =  π(4)²

Step 3 :

Since radius is not a multiple of 7, we can use π  ≈  3.14.

Area of the circle  ≈  (3.14) x (4)²

Area of the circle  ≈  3.14 x 16

Area of the circle  ≈  50.24 square cm. 

The area of the biscuit is about 50.24 square cm.

Question 4 :

Compare finding the area of a circle when given the radius with finding the area when given the diameter.

Answer :

The formula for area of a circle uses the radius of the circle. If we are given the diameter of the circle, we must first divide it by two to get the radius.

Question 5 :

Why do we evaluate the power in the equation before multiplying by pi ?

Answer :

We must follow the order of operations and evaluate the exponents before multiplying.

Question 6 :

When is it logical to use 22/7 instead of 3.14 for π ?

Answer :

When the radius or diameter is a multiple of 7

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