If the area of the base of a cone is 770 $ \displaystyle cm^{2} $and the curved surface area is 814 $ \displaystyle cm^{2} $ then its volume is

Using the base area of pi times r squared, the radius is found by dividing 770 by the approximate value of pi, 22 divided by 7, resulting in a radius of 7 times the square root of 5. The curved surface area is pi times r times l, where l is the slant height, so 814 divided by 22 divided by 7 multiplied by 7 times the square root of 5 gives a slant height of 37. Finding the height with the Pythagorean theorem yields the square root of 37 squared minus the square of 7 times the square root of 5, which simplifies to the square root of 1369 minus 245, or 34. Applying the cone volume formula of one third times pi times r squared times h gives one third times 770 times 34, resulting in 616 times the square root of 5.

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