Question

Two similar cones have radii of 9 and 1, respectively. what is the ratio of their volumes?

Answer 1

Ratio f their volumes = ratio of the cubes of radii

so its  9^3 : 1^3  = 729:1

Answer 2

Solution:

The ratio of the volumes is 81:1

Explanation:

We have been given that the radii of two similar cones are in the ratio 9:1.

Let a be the radius of first cone and b be the radius of second cone. Then, we have

$\frac{a}{b} =\frac{9}{1}$

The volume of the cone is given by

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

Since, the cones are similar hence, the ratio of volume of these cone is equal to the ratio of the square of the radius.

Thus, the ratio of volume is given by

$\frac{V_1}{V_2} =\frac{a^2}{b^2} \\\\\frac{V_1}{V_2} =(\frac{a}{b} )^2\\\\\frac{V_1}{V_2} =(\frac{9}{1} )^2\\\\\frac{V_1}{V_2} =\frac{81}{1}$

Therefore, the ratio of the volumes is 81:1