Video: Finding the Areas of Circles

Given that the inner radius is 6.5 cm and the outer radius is 11.5 cm, use 3.14 in place of ๐œ‹ to find the area of the colored region.

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Video Transcript

Given that the inner radius is 6.5 centimeters and the outer radius is 11.5 centimeters, use 3.14 in place of ๐œ‹ to find the area of the colored region.

So we have a diagram of a small circle within a larger circle, and the two circles have the same center. Weโ€™re told the inner radius is 6.5 centimeters and the outer radius is 11.5 centimeters. We need to find the area of the colored region. So in order to do this, weโ€™re going to find the area of the larger circle and then subtract the area of the smaller circle. We need to accure the formula for calculating the area of a circle. Area is equal to ๐œ‹ multiplied by ๐‘Ÿ squared, where ๐‘Ÿ is the radius of the circle.

Letโ€™s begin our calculation. For the large circle first of all, remember weโ€™re told to use 3.14 in place of ๐œ‹. So we have 3.14 multiplied by 11.5 squared. For the smaller circle, we have 3.14 multiplied by 6.5 squared. Now we need to evaluate each of these areas. We have 415.265 minus 132.665.

This is equal to 282.6 and the units for this area are centimeters squared.

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