Area :
Area of a circle is defined as the space occupied by the circular object on a flat surface. The area of a shape can be measured by comparing the shape to squares of a fixed size.
Circumference :
The perimeter of a circle is called its circumference. In other words, the distance around the edge of a circle.
The measurements of perimeter use units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The measurements of area use units such as square centimeters (cm^{2}), square meters(m^{2}), and so on.
Example 1 :
An irrigation sprinkler waters a circular region with a radius of 14 feet. Find the circumference of the region watered by the sprinkler. Use 22/7 for π.
Solution :
Use the formula.
C = 2πr
Substitute 14 for r.
C = 2π(14)
Substitute 22/7 for π.
C ≈ 2 x (22/7) x 14
Simplify
C ≈ 2 x (22/1) x 2
C ≈ 88
So, the circumference of the region watered by the sprinkler is about 88 feet.
Example 2 :
The diameter of a car wheel is 21 inches. Find the circumference of the wheel.
Solution :
Radius = Diameter / 2
Radius = 21/2 inches
Use the formula.
C = 2πr
Substitute 21/2 for r.
C = 2π(21/2)
Substitute 22/7 for π.
C ≈ 2 x (22/7) x (21/2)
Simplify.
C ≈ 2 x (11/1) x (3/1)
C ≈ 66
So, the circumference of the wheel is 66 inches.
Example 3 :
Find the diameter, radius, circumference and area of the circle shown below. use 3.14 as an approximation for π.
Solution :
From the diagram shown above, we can see that the diameter of the circle is
d = 13 - 5 = 8 cm
The radius is one half the diameter. So, the radius is
r = d/2 = 8/2 = 4 cm
Using the formula for circumference, we have
C = 2πr ≈ 2(3.14)4
C ≈ 25.1 cm
Using the formulas for area, we have
A = πr^{2} ≈ (3.14)(4)^{2}
A ≈ 50.24 square cm.
Example 4 :
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 4 for r 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.
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