Find the area of the following circle. ( = 3.14; round answer to the nearest whole number). Circumference = 120 cm. (Hint: Find r from C = 2r (round r to tenths); then find area).
2 pi r = 120
r = 60/pi
pi r^2 = pi (60^2/pi^2) = 3600/pi
=1146 cm^2
To find the area of a circle, you will need to follow a few steps.
Step 1: Find the radius (r) of the circle using the formula C = 2πr, where C is the circumference.
In this case, the given circumference is 120 cm.
120 = 2πr
To isolate r, divide both sides of the equation by 2π:
r = 120 / (2π)
Step 2: Calculate the value of r to the nearest tenth.
Using the value of π given as 3.14, substitute it into the equation:
r = 120 / (2 * 3.14)
r ≈ 120 / 6.28
r ≈ 19.11
Rounding this value to the nearest tenth, we get:
r ≈ 19.1 cm
Step 3: Calculate the area of the circle using the formula A = πr^2, where A is the area.
Substitute the calculated radius (r ≈ 19.1 cm) into the formula:
A = 3.14 * (19.1)^2
A ≈ 3.14 * 365.21
A ≈ 1146.37
Rounding the result to the nearest whole number, we get:
A ≈ 1146
Therefore, the area of the circle is approximately 1146 square units.