Question

Cylinder A is similar to cylinder B, and the radius of A is 3 times the radius of B. What is the ratio of: The lateral area of A to the lateral area of B?
What is the ratio of: The volume of A to the volume of B?

Answer 1

Let radius of cylinder A be Ra,
And that of cylinder B be Rb,
Given that Ra=3Rb;
Lateral surface area of cylinder is 2(pi)rh;
If taken ratio, since 2,(pi),h is const they get cancelled; ratio of LSA=Ra:Rb=3:1.
Volume of a cylinder =(pi)r^2h,
Here, (pi),h is const;
=>ratio of volumes=Ra^2:Rb^2,
=>Ra^2:(Ra/3)^2.
=>Ra^2:Ra^2/9
=>1:1/9, or 9:1.