The circumference 𝐶 of a circle can be estimated using the formula 𝐶 equals forty-four sevenths 𝑟, where 𝑟 is the radius. Find an estimate of the radius of a circle with 𝐶 equals 67.1. Round your answer to the nearest tenth.
We’re given this formula 𝐶 equals 44 over seven 𝑟 to estimate circumference. And then we’re given the circumference of a circle. And it’s asking us to estimate the radius.
We’ll take the circumference given, 67.1, set it equal to forty-four sevenths times the radius. To find the radius, we’ll need to get 𝑟 by itself.
We can do that by multiplying both sides of the equation by seven over 44. Seven over 44 cancels out forty-four sevenths. And that leaves us with the radius isolated on the right and seven times 67.1 divided by 44 on the left. Seven times 67.1 equals 469.7. We need to divide that number by 44.
When we do that, we get a radius that’s equal to 10.675. We need this value to the nearest tenth. The digit to the right of the tenths place is a seven, which means we round this six up to a seven. And everything to the left of the tenths place stays the same. The radius rounded to the nearest tenth is 10.7.