Relating Area to Circumference

Student Summary

If CC is a circle’s circumference and rr is its radius, then C=2πrC=2\pi r. The area of a circle can be found by taking the product of half the circumference and the radius.

If AA is the area of the circle, this gives the equation:

A=12(2πr)rA = \frac12 (2\pi r) \boldcdot r

This equation can be rewritten as:

A=πr2A=\pi r^2

Remember that when we have rrr \boldcdot r we can write r2r^2, and we can say “rr squared.”

This means that if we know the radius, we can find the area. For example, if a circle has a radius of 10 cm, then its area is about (3.14)100(3.14) \boldcdot 100, which is 314 cm2.

If we know the diameter, we can figure out the radius, and then we can find the area. For example, if a circle has a diameter of 30 ft, then the radius is 15 ft, and the area is about (3.14)225(3.14) \boldcdot 225, which is approximately 707 ft2.

Visual / Anchor Chart

Standards

Addressing
7.G.4

7.G.B.4

7.G.4

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7.G.4

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