Question

a cylinder has radius R and height H if the radius and the height of a cylinder are doubled then a new cylinder is obtained find the ratio of curved surface area of original cylinder to that of a new cylinder​

Answer 1

In order to find the volume of a cylinder, you would use the formula V=3.14*r2*h.  In the formula, the radius is being squared.  That means that doubling the radius of the cylinder will quadruple the volume.  For example, let's say we have a cylinder with a radius of 2 inches and height of 3 inches.  The volume would be 3.14*22*3 = 3.14*4*3 = 37.68 in2.  However, doubling the radius would have this effect: 3.14*42*3 = 3.14*16*3 = 150.72 in2.  That is four times as large as the original volume.  Now, because the height is not squared in the original formula, doubling the height of a cylinder will just double the volume.  If we put all of that information together (doubling the radius quadruples the volume, while doubling the height doubles the volume), we find that the volume will be 8 times as large.  This is because the radius multiplies the volume by four and the height multiplies the volume by 2, and 4*2=8.