Question

The height of two cones are in the ratio 7:3 and their diameter are in the ratio 6:7 what is the ratio of there volumes

Answer 1

$9 \times 7 = 12.25 \times 3 \\ \\ 63 = 36.75 \\ \\ so \: answer \: is \: \frac{21}{12.25}$

21:12.25

Answer 2

Concept:

The volume of a cone is

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

Given:

The ratio of heights of the two cones = 7:3

The ratio of diameters is 6:7

To find:

The ratio of the volumes

Solution:

In this question, the ratio of heights of the two cones = 7:3

The ratio of diameters is 6:7 is given to us

Let the heights are x and the diameters are y

Then the heights of the two cones are 7x and 3x and their radii are 6y and 7y

So, if we put the volumes of both the cones proportional to one other then we get

$\frac{\frac{1}{3}\pi *(6y^{2})*7x }{\frac{1}{3} \pi *(7y^{2})*3x } \\\frac{36*7}{49*3} \\\frac{12}{7} \\12:7$

Hence, the ratio of the volumes is 12:7

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