What is the volume of larger cylinder in the following case?Two cylinders are similar. The lateral areas of the cylinders are 196*pi square...

We have two similar cylinders, this means the ratio of
their radius is equal to the ratio of their height.

The
lateral area of the cylinder are 196*pi and 342*pi. The lateral area of a cylinder with
a radius equal to r is pi*r^2. Let the radius of the cylinders be r1 and
r2.

196*pi / 324*pi = pi*r1^2 /
pi*r2^2

=> 196/324 =
(r1/r2)^2

=> r1/r2 = 14 / 18 =
7/9

The radius of the larger cylinder is 9/7 times that of
the smaller cylinder. As the two cylinders are similar their height is also in the same
ratio. Let the height of the smaller cylinder be h, the height of the larger cylinder is
(9/7)*h

The volume of a cylinder with height h and radius r
is pi*r^2*h

=> lateral area *
h

For the smaller cylinder, the volume is
686*pi

=> 196*pi*h =
686*pi

=> h = 686*pi /
196*pi

=> h =
686/196

=> h = 3.5

This
gives the height of the larger cylinder as
(9/7)*3.5

=> 4.5 cm

The
volume of the larger cylinder is 4.5*324*pi = 1458*pi
cm^3

The volume of the larger cylinder is
1458*pi cm^3