Question

 Two cones have their base radii in ratio of 3 : 1 and the ratio of their heights as 1 : 3. Find the ratio of their volumes.​

Answer 1

Answer:

The ratio of heights of cone is 1:3.

The ratio of radius of cone is 3:1.

We know that the volume of the cone,

V=31πr2h

Therefore,

V2V1=31πr22h231πr12h1

V2V1=r22h2r12h1

V2V1=1×39×1

V2V1=13

Hence, the ratio of the volume of this cone is 3:1.

Step-by-step explanation:

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Answer 2

Answer:

Ratio of radii=3:1

therefore let radii be 3x and x

Ratio of height=1:3

therefore let height be y and 3y

therefore

V1=1/3pie*r^2*h

=1/3pie *((3x)^2)*(y)

=1/3pie *(9x^2)*(y)

therefore

V2=1/3pie*R^2*H

=1/3pie*(x^2)*(3y)

therefore

V1/V2=[1/3pie*(9x^2)*(y)]/ [1/3pie*(x^2)*(3y)]

=(9x^2*y)/(x^2*3y). [1/3pie gets cancelled]

=9/3. [x^2*y. gets cancelled]

=9:3=3:1

therefore the ratio of the volumes is 3:1

Hope it helps