The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. Find the ratio of its height to the diameter .

Suppose r and h be the radius and the height of the cylinder respectively.
So, curved surface area of cylinder = 2πrh = 264 m2
2rh = 264π2rh = 264×722 = 84 .....(i)
And volume of cylinder = πr2h = 924 m3
r2h = 924πr2h =924×722 = 294 ....(ii)
Dividing (ii) by (i) we get;
r2h2rh = 29484r2 = 29484r = 29484×2 = 7
So, radius of cylinder is 7 m.
Then its diameter = 2×7 = 14 m
Putting the value of r in (i) we get;
2×7h = 84h = 842×7 = 6
So height of cylinder is 6 m.
so the ratio of height to the diameter = 614 = 37
Therefore the ratio of height to the diameter  is 3 : 7.

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