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The curved surface area of a cylindrical pillar is $264$ sq.cm and its volume is $924$ cubic cm. The ratio of its diameter to its height is:

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3 : 7

7 : 3

6 : 7

7 : 6

answer is B.

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Detailed Solution

Let the radius of the cylindrical pillar be r and height h.
We know,
Curved Surface Area of the cylinder

= 2 π r h

Substituting values in above formula. We have,

264 = 2 × 227 × r × h ⇒ r × h = 264 × 722 × 12 ⇒ r h = 132 × 722 ⇒ r h = 6 × 7 ⇒ r h = 42....................... (i)

Also, volume of cylinder is given as,

V = π r 2 h

.
Substituting values in above formula. We have,

924 = 227 × r 2 × h ​ ⇒ r 2 × h = 924 × 722 ​ ⇒ r 2 h = 42 × 7 ​ ⇒ r 2 h = 294.................... (i i) ​

Dividing (ii) by (i) we have

r 2 h r h = 29442 ⇒ r = 7

Now, substituting the value of r in equation (i) to get the value of h.

r h = 42 ​ ⇒ 7 (h) = 42 ​ ⇒ h = 427 ​ ⇒ h = 6 ​

Therefore, from above we see that the radius of the cylinder is 7 cm and height is 6 cm.
From above diameter of cylinder is =

(2 r)

Diameter of cylinder is =

2 × 7 = 14 c m

Now, to find the ratio of diameter to height. We have,

d i a m e t e r h e i g h t = 146 ​ ⇒ d i a m e t e r h e i g h t = 73 ​

Hence, from above we see that ratio of diameter to its height is

7 : 3

.
So, option 2 is correct.

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