Question

12. If two cylinders of same lateral surface have their radii in the ratio 4:9, then the ratio of
their heights is
(a) 2:3
(6) 3:2
(c) 4:9
(d) 9:4​

Answer 1

Answer:

a. 2:3 is the correct answer

Step-by-step explanation:

Two cylinders have the same lateral surface area. There radii are in the ratio 3:2. What is the ratio of the height of the 1st cylinder to that of the 2nd cylinder?

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As their radii are in the ratio 3:2

Let them be 3x and 2x

Let Height of first cylinder=h

And Height of second cylinder=H

ATQ

2πrh=2πRH

3xh=2xH

h/H=2x/3x

h/H= 2/3

Hence, the answer is 2/3…

Hope this helps :-)

Let the two cylinders be C1 and C2, their radii R1 and R2 and their heights H1 and H2.

Let R1 = 3R and R2 = 2R

Lateral surface area of C1 = 2(pi)R1H1

Lateral surface area of C2 = 2(pi)R2H2

Now the Lateral surface areas of the two are the same, therefore

2(pi)R1H1 = 2(pi)R2H2 or

R1H1 = R2H2. Substituting for R1 and R2

3RH1 = 2RH2. Or

3H1 = 2H2

Hence H1 = (2/3)H2

The height of the first cylinder is two-thirds that of the second.