Question Video: Finding the Diameter of a Sphere given Its Surface Area Mathematics • 8th Grade

What is the diameter of a sphere whose surface area is 36๐œ‹ cmยฒ?

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Video Transcript

What is the diameter of a sphere whose surface area is 36๐œ‹ square centimeters?

In this question, weโ€™ve been given the surface area of a sphere and asked to use this to determine its diameter. We recall that the general formula for finding the surface area of a sphere is four ๐œ‹๐‘Ÿ squared. So by equating these two pieces of information, we can form an equation that will enable us to determine firstly the radius of the sphere. We have the equation four ๐œ‹๐‘Ÿ squared equals 36๐œ‹. And we can now solve this equation. Firstly, we can cancel a factor of ๐œ‹ on each side. We can then divide each side of the equation by four to leave ๐‘Ÿ squared on the left-hand side and nine on the right-hand side. So we now have the equation ๐‘Ÿ squared is equal to nine.

We solve this equation by square rooting. And weโ€™re only going to take the positive value here because ๐‘Ÿ has a physical meaning as the radius of the sphere. Nine is a square number, and its square root is three. So we found that the radius of the sphere is three centimeters. We must be careful, though, because it wasnโ€™t the radius of the sphere that we were originally asked to find. It was the diameter. But thatโ€™s no problem because we know that the diameter of a sphere is twice its radius. So if the radius is three, the diameter will be six. Weโ€™ve solved the problem, and the diameter of the sphere whose surface area is 36๐œ‹ square centimeters is six centimeters.

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