Question

The height of 2 cones are in the ratio 1 : 5 and their radii are in

the ratio 5:7. Find the ratio of their volumes.​

Answer 1

Given that :

The height of 2 cones are in the ratio of 1:5 and their radii are in the ratio of 5:7

Let, the heights of the cones be H and 5H and their radii be 5R and 7R

As we know that :

The volume of cone = 1/3 πr^2h,

where r = radius of cone

and h = Height of the cone

Now, The volume of first cone = 1/3 π(5R)^2.5H

=> The volume of first cone = 125.1/3.πR^2H.... (1)

And The volume of second cone = 1/3 π(7R)^2.5H

=> The volume of second cone = 245.1/3.πR^2H...(2)

To find :

The ratio of volume of the cones = ?

According to the question :

Equation (1) ÷ Equation (2)

=> [ 125.1/3.πR^2H ] ÷ [ 245.1/3.πR^2H ]

=> 125 ÷ 245

=> 25 ÷ 49

So, the ratio of the volume of cones will be 25 : 49

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Hope it helps !!