Question

Two cones have their radii in ratio of 3 raise to 1 in the ratio of their Heights is 1 raise to 3 find the ratio of their volumes

Answer 1

Hey mate..

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Let the height of the cones be h1 and h2 respectively.

Given,

h1 : h2 = 1:3

Also, 

Let the radii of the two cones be r1 and r2 respectively.

Given,

r1 : r2 = 3:1

We know,

Volume of a cone = \frac{1}{3} \pi \: r {}^{2} h31πr2h 

A/Q,

\frac{ \frac{1}{3}\pi \: r1 {}^{2} h1}{ \frac{1}{3}\pi \: r2 {}^{2} h2}31πr22h231πr12h1 ..........(1)

By substituting the values in Eq.(1) we get,

\frac{(3) {}^{2} \times 1 }{(1) {}^{2} \times 3}(1)2×3(3)2×1 

= \frac{9 \times 1}{1 \times 3}1×39×1 

= \frac{9}{3}39 

= \frac{3}{1}13 

= 3:1

Thus,

The ratio of their volumes = 3:1 

(Hence proved )

#racks

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