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 = πr^{2} |
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 = πr^{2}
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 = πr^{2}
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 = πr^{2}
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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