Question

area of circles
formula for area of circle
area of a circle with radius of r units is
a = πr²
use π = 3.14 or 22/7.
do not use the π button on your calculator!
example a: find the area of the circle with radius of 3 units.
a = πr²
= π(radius)(radius) = (3.14)(3)(3)
= (3.14)(9) = 28.26 sq. units
example b: find the area of the circle with a diameter of 10 units.
the formula for the area of a circle uses the length of the radius, not the diameter.
we must first divide the diameter by 2 to find the length of the radius.
if the diameter is 10 units, the radius is 5 units.
a = πr²
= (3.14)(5)(5)
= (3.14)(25) = 78.5 sq. units
exercises: find the area of each circle.
1.) radius = 15 cm. area = ________
2.) diameter = 8 mm. area = ________
3.) area = ________
4.) area = ________
5.) area = ________
6.) area = ________

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius of the circle. If the diameter \(d\) is given, then \(r = \frac{d}{2}\).

Step2: Solve for problem 1

Given \(r = 15\space cm\), \(A=\pi r^{2}\). Using \(\pi=3.14\), \(A = 3.14\times15\times15=3.14\times225 = 706.5\space cm^{2}\)

Step3: Solve for problem 2

Given \(d = 8\space mm\), then \(r=\frac{d}{2}=\frac{8}{2}=4\space mm\). \(A=\pi r^{2}=3.14\times4\times4=3.14\times16 = 50.24\space mm^{2}\)

Step4: Solve for problem 3

Given \(r = 21\space in\), \(A=\pi r^{2}\). Using \(\pi = 3.14\), \(A=3.14\times21\times21=3.14\times441=1384.74\space in^{2}\)

Step5: Solve for problem 4

Given \(d = 14\space ft\), then \(r=\frac{d}{2}=\frac{14}{2} = 7\space ft\). \(A=\pi r^{2}=3.14\times7\times7=3.14\times49 = 153.86\space ft^{2}\)

Step6: Solve for problem 5

Given \(r = 5.1\space in\), \(A=\pi r^{2}\). Using \(\pi=3.14\), \(A=3.14\times5.1\times5.1=3.14\times26.01 = 81.6714\space in^{2}\)

Step7: Solve for problem 6

Given \(d = 58\space mm\), then \(r=\frac{d}{2}=\frac{58}{2}=29\space mm\). \(A=\pi r^{2}=3.14\times29\times29=3.14\times841 = 2640.74\space mm^{2}\)

Answer:

1. \(706.5\space cm^{2}\)
2. \(50.24\space mm^{2}\)
3. \(1384.74\space in^{2}\)
4. \(153.86\space ft^{2}\)
5. \(81.6714\space in^{2}\)
6. \(2640.74\space mm^{2}\)