Question

If two pyramids are similar and the ratio between the lengths of their edges is 4:9, what is the ratio of their volumes?

Answer 1

The answer is 64:729

Answer 2

Answer:

Ration between the volumes = 64:729

Step-by-step explanation:

If two pyramids are similar and ratio between the lengths of their edges is 4:9

Then we have to tell the ration between their volumes.

Since volume of pyramid $V=\frac{1}{3}l.w.h$

Let length and width of pyramid one are l and w.

So volume of one pyramid $V_{1}=\frac{1}{3}.l.w.h$

Now by the ratio of 4:9, edges of the second pyramid will be

$L_{2}=\frac{4l}{9}$

$W_{2}=\frac{4}{9}w$

$H_{2} =\frac{4}{9}h$

Therefore volume of second pyramid  $V_{2}=\frac{L_{2}.W_{2}.H_{2} }{3}=\frac{\frac{4l}{9}.\frac{4w}{9}.\frac{4h}{9}}{3}=(\frac{1}{3})(\frac{64}{729})l.w.h$

Now ratio of volumes of both the pyramids = $\frac{V_{2} }{V_{1}}=\frac{(\frac{64}{729})(\frac{1}{3} )l.w.h}{\frac{1}{3}l.w.h}= 64:729$

Answer is 64:729 will be the ratio of their volumes.