Question

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

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Answer 1

Answer:

The ration is 3:1....

Step-by-step explanation:

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Answer 2

Solution

Given :-

• Two cones have their heights in the ratio 1 : 3
• radii of their bases in the ratio 3:1

Find :-

• The ratio of thier volume

Explanation

Let,

• Height of first cone = H
• Height of second cone = H'

And,

• Base raddi of first cone = R
• Base raddi of second cone = R'

According question,

• Height of first cone = H = x
• Height of second cone = H' = 3x

And,

• Base raddi of first cone = R = 3y
• Base raddi of second cone = R' = y

Using Formula

$\dag\boxed{\underline{\tt{\blue{\:Volume_{cone}\:=\:\dfrac{\pi\:r^2h}{3}}}}}$

For First Cone,

==> Volume of first cone (V) = π.(3y)².x/3

==> Volume of first cone (V) = 9πy²x/3

For second Cone

==> Volume of second cone (V') = π.y².3x/3

==> Volume of second cone (V') = 3πxy²/3

Now, calculate ratio of first & second cone.

==> Ratio of thier volume = Volume of first cone/Volume of second cone

==> Ratio of thier volume = ( 9πxy²/3)/(3πxy²/3)

==> Ratio of thier volume = 9πy²x/3πxy²

==> Ratio of thier volume = 3/1

or,

==> Ratio of thier volume = 3:1

Hence

• Ratio will be thier volume of cone = 3:1

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