Question

two cones have their height in the ratio 1:3 and the radii of their bases in the ratio 3:1show that their volume are in the ratio 3:1

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 = $\frac{1}{3} \pi \: r {}^{2} h$

A/Q,

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

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

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

= $\frac{9 \times 1}{1 \times 3}$

= $\frac{9}{3}$

= $\frac{3}{1}$

= 3:1

Thus,

The ratio of their volumes = 3:1

(Hence proved )

#racks

Answer 2

Answer:

I hope it will help you to understand .