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How to Find Diameter from Area of a Circle | Geometry, Diameter Given Area
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How do we find the diameter of a circle given the area? We'll go over the general formula for finding diameter from area and how to apply it in today's video geometry lesson!
Remember that the area of a circle is A = pi*r^2 where r is the radius length: the distance from the center to any point on the circle. Then, we just solve for r to find that r = sqrt(A/pi), this is how we can find the radius from the area. Then we just multiply both sides by 2 since the diameter, d, is two times the radius! So d = 2r = 2*sqrt(A/pi).
SOLUTION TO PRACTICE PROBLEM:
The area is given as 5 meters. Thus, the radius r is r = sqrt(5m / pi), or we could round it to 1.3 m.
Double the radius to get the diameter, d, d = 2*r = 2*sqrt(5m / pi). The answer could be left exact in this form, or rounded to 2.5 m. Note that if we rounded the radius to 1.3 m and then doubled that, we would get 2.6 m as the diameter, which is pretty off from the exact answer.
Remember to avoid rounding as much as possible until you arrive at the end of the problem! If we only wanted the radius, then rounding it to 1.3 m may be fine. But if we want diameter, then we should hold off on the rounding until we get the diameter. The approximations were done using 3.14159 in place of pi.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
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Remember that the area of a circle is A = pi*r^2 where r is the radius length: the distance from the center to any point on the circle. Then, we just solve for r to find that r = sqrt(A/pi), this is how we can find the radius from the area. Then we just multiply both sides by 2 since the diameter, d, is two times the radius! So d = 2r = 2*sqrt(A/pi).
SOLUTION TO PRACTICE PROBLEM:
The area is given as 5 meters. Thus, the radius r is r = sqrt(5m / pi), or we could round it to 1.3 m.
Double the radius to get the diameter, d, d = 2*r = 2*sqrt(5m / pi). The answer could be left exact in this form, or rounded to 2.5 m. Note that if we rounded the radius to 1.3 m and then doubled that, we would get 2.6 m as the diameter, which is pretty off from the exact answer.
Remember to avoid rounding as much as possible until you arrive at the end of the problem! If we only wanted the radius, then rounding it to 1.3 m may be fine. But if we want diameter, then we should hold off on the rounding until we get the diameter. The approximations were done using 3.14159 in place of pi.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
+WRATH OF MATH+
Follow Wrath of Math on...
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