Question

the lateral surface area of a cylinder is equal to the curved surface area of a cone If their bases be the same find the ratio of the height of the cylinder to the slant height of the cone

Answer 1

Answer:

Let, the lateral surface area of cylinder be 2πr1h

curved surface area of cone =πr2l

Given:

2πr1h=πr2l

also r1=r2

Therefore,

2h=l

h/l= 1/2

Answer 2

The ratio of height of cylinder to slant height of cone is 1:2

Given:

L.S.A of cylinder = to C.S.A of cone  

Where,

L.S.A = lateral surface area,

C.S.A= curved surface area

To find:

The ratio between height of cylinder and the cone’s slant height.

Solution:

Let the radius be r, height be h, length be l

Given their base are equal, hence their radius is same

By formula, the lateral surface area of the cylinder =  2πrh

By formula, the curved surface area of cone = πrl

Hence 2πrh = πrl

2h = l

$\frac{h}{l}=\frac{1}{2}$

The ratio of height of cylinder to slant height of cone = 1 : 2