What is the approximate area of a circle with a diameter of 18 m?

Answer 1

254 in

Answer 2

Since the question asks for an approximate value, and not an exact value, we can assume that 18 meters is an approximate measurement, and not an exact value. Thus, we can use the formula for the area of a circle: Area = pi * (radius)^2 and then round off the final answer to the amount of significant digits that we put into the formula, the 2 significant digits of 18 m. We only round off the final answer; we try to use as many digits as possible in the steps in between so that we don't introduce errors.

For example, to get the radius of the circle, we halve the diameter, so the radius of the circle is 9 meters. We use the formula now by applying order of operations. First we evaluate the exponent by squaring the radius to get 81 square meters. Then we multiply this by a value of pi that has as many accurate digits as possible. I used a calculator to get 254.46900494077325231547411404564 square meters. This is a ludicrous amount of detail from a measurement of only 2 significant digits. Since we only have 2 significant digits of information, we only know that the first two digits of our answer are accurate: 25_.___.... . This means the true area is between 250 and 260 (all the numbers that start with 25_). We do not have enough information to determine the third digit, but since the next digit in our ideal calculation is 4, then if the true diameter is closer to exactly 18.0 meters, then the true area is closer to 250 than 260, so we report the approximate area as 250 square meters.