Question

Find the area of the following circle. (round answer to the nearest whole number.) circumference = 280 cm. (hint: find r from c = 2pr (round r to tenths); then find area).

1) 89
2) 560
3) 1,989
4) 6,246

Answer 1

To find the area of a circle given the circumference, the radius is first calculated using the formula C = 2πr, and then the area is computed with the formula A = πr². Using the given circumference of 280 cm, we find the area to be approximately 6,246 cm² when rounded to the nearest whole number.

Step-by-step explanation:

To find the area of a circle given its circumference, first, we need to calculate the radius. The relationship between the circumference (C) and the radius (r) of a circle is given by the formula C = 2πr, where π (pi) is approximately 3.14159. Once we have the radius, we can compute the area (A) of the circle using the formula A = πr².

In the question given, the circumference is 280 cm. To find the radius, we rearrange the formula:

r = C / (2π)

Substitute the known values:

r = 280 cm / (2 × 3.14159)
r ≈ 44.6 cm

Now that we have the radius, we can proceed with finding the area of the circle:

A = πr²
A = 3.14159 × (44.6 cm)²
A ≈ 6,246 cm²

The area should be rounded to the nearest whole number, as instructed, thus A ≈ 6,246 cm².