Question

Two cylinder have same lateral surface area. Their radii are in ratio 3:3. Find the ratio of their Heights.

Answer 1

Answer:

1:1

Step-by-step explanation:

$\text{Ratio of Radii = 3:3}\\\\\text{Let Radii be 3x and 3x, ie, radii are equal}\\\\\text{Also, their Lateral Surface Area are same. Hence, Ratios of Lateral Surface Areas = 1:1}\\\\\text{Formula for CSA of Cylinder = 2} \pi r h\\\\\text{Let height of first cylinder be h and of second be H.}\\\\\text{Now, CSA of cylinder with height h = 2} \pi 3x h\\\\\text{And, CSA of cylinder with height H = 2} \pi 3x H\\\\\text{Ratios of CSAs = } \dfrac{2 \pi 3x h}{2 \pi 3x H} = \dfrac{h}{H}$

$\text{But, calculated ratio of CSA = 1:1}\\\\\implies h:H = 1:1\\\\\implies \text{Ratio of Heights h and H is 1:1. This means they have equal values.}$

Hope it helps!