Question

A circles circumference is 600m. What is a good approximation of the circles area

Answer 1

28 662 m²

Explanation:

The formula for the area of a circle is A = πr².

The formula for the circumference is C = 2πr.

We know that C = 600 m, so we can use that number to find r, and then insert it into the formula for the area.

Let's see how far we can get into solving the problem before we must make an approximation.

The calculations

(a) Solve for r

`\begin{array}{rcl}C & = & 2\pi r\\600 & = & 2 \pi r\\300 & = & \pi r\\r & = & (300)/(\pi)\\\end{array}`

(b) Use this value of r to calculate the area

`\begin{array}{rcl}A & = & \pi r^(2)\\& = & \pi \left ((300)/(\pi)\right)^(2)\\& = & \pi* (90000)/(\pi^(2))\\& = & (90000)/(\pi)\\\end{array}`

(c) Approximate the area

We must make approximation for π.

We could make a rough approximation and say that π is about 3.

That would give an area of about 30 000 m².

However the question asks for a "good" approximation, so we should probably say that π is about 3.14.

Using that number, we get

`A = (90000)/(3.14) = \textbf{28 662 m}^{\mathbf{2}}`