# Video: Estimating the Radius of a Circle given Its Circumference Using a Given Formula for That Circumference

The circumference 𝐶 of a circle can be estimated using the formula 𝐶 = 44/7 (𝑟), where 𝑟 is the radius. Find an estimate of the radius of a circle with 𝐶 = 67.1. Round your answer to the nearest tenth.

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### Video Transcript

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 61.1 [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.