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

Ration between the volumes = 64:729

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=(1)/(3)l.w.h`

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

So volume of one pyramid
`V_(1)=(1)/(3).l.w.h`

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

`L_(2)=(4l)/(9)`

`W_(2)=(4)/(9)w`

`H_(2) =(4)/(9)h`

Therefore volume of second pyramid
`V_(2)=(L_(2).W_(2).H_(2) )/(3)=((4l)/(9).(4w)/(9).(4h)/(9))/(3)=((1)/(3))((64)/(729))l.w.h`

Now ratio of volumes of both the pyramids =
`(V_(2) )/(V_(1))=(((64)/(729))((1)/(3) )l.w.h)/((1)/(3)l.w.h)= 64:729`

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