Question

the radius of a cylinder is doubled and height remains the same. the ratio between the volume of the new cylinder and the original cylinder is​

Answer 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.

Answer 2

Answer:

Step-by-step explanation: Let the original radius be r,

If original volume be, V1,

Then, V1 = π r²h .............(1)

(Where, h is the height of the cylinder)

Now , if the new radius be 2r,

If  new volume be, V2

Then, V2 = π (2r)²h ...............(2)

On dividing eq. (2) by (1),

V1/V2 = (π(2r)²h)/ ( πr²h)

V1/V2 = 4r²/r²

VI/V2 = 4/1

Therefore, the ratio between the volume of new cylinder and the original cylinder is 4 : 1. (Ans.)

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