Question

The radius of a cylinder is doubled and the height remains the same. The ratio between the volumes of the

new cylinder and the original cylinder is

(a) 1 : 2(b) 3 : 1

(c) 4 : 1(d) 1 : 8​

Answer 1

Option (c) 4 : 1.

To Find :-

• The ratio between the volumes of the new cylinder and original cylinder.

Solution :-

The radius of a cylinder is doubled and the height remains the same. (Given)

↪ Radius of original cylinder = r

↪ Radius of new cylinder = 2r

↪ Height remains the same.

We know that,

↪ Volume of cylinder = πr²h

[ For original cylinder ]

↪ Volume of original cylinder = r²πh

[ For new cylinder ]

↪ Volume of new cylinder = π(2r)²h

↪ Volume of new cylinder = 4r²πh

Now

Let ratio of there volume be " x ".

Ratio of there volume = Volume of new cylinder / Volume of original cylinder

[ Put the values ]

↪ x = 4r²πh / r²πh

↪ x = 4r² / r²

↪ x = 4 / 1

↪ x = 4 : 1

Therefore,

The ratio between the volumes of the new cylinder and original cylinder is 4 : 1.