A sphere of radius r has the same total surface area as a solid cylinder of a base
radius r and height h.Find the ratio of their volumes. (ans:4:3)
Maths ( Ratio)
2008-08-08 11:18 pm
回答 (1)
2008-08-08 11:32 pm
✔ 最佳答案
Surface area of the sphere = 4(pi)r^2.Surface area of the cylinder = 2(pi)r^2 + 2(pi)rh
So 4(pi)r^2 = 2(pi)r^2 + 2(pi)rh
2(pi)r = 2(pi)h
h = r
Therefore, volume of cylinder = (pi)r^2(r) = (pi)r^3 = (pi)r^3.
So ratio of volume = 4(pi)r^3/3 : (pi)r^3
= 4:3.
收錄日期: 2021-04-25 22:37:28
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