Question

The curve surface are of a cylinder is 264 m2 and its volume is 924m3 find the ratio of its height to its diameter.

Answer 1

Let the radius of base be r

and height be h

According to question,

C.S.A = 264

2 pi r h = 264 -----(1)

and ,

Volume = 924

pi r^2 h = 924 ------(2)

On dividing equation (2) by (1), we get

r / 2 = 3.5

r = 7 m

Diameter = 2 × 7 = 14 m

Now,

On putting the value of r in equation (1) , we get

2 × 22 × 7 × h / 7 = 264

=> 44h = 264

=> h = 6 m

Required ratio = 6 / 14

= 3 : 7

Answer 2

C.S.A.=2πrh
264=2×22/7×rh
264×7/44=rh
42=rh-----(1)

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Volume=πr²h
924m³=22/7×r²h
294=r²h------(2)

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Dividing both equation
r²h/rh=294/42
r=7m
d=2r
d=14m

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Putting r in equation 1
7h=42
h=6

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6/14
3:7