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...

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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**