Question

The ratio of the height of two similar pyramids is 4:7. The volume of the smaller pyramid is 1,331cm, to the nearest whole number, what is the volume of the larger pyramid ?

Answer 1

The volume of the larger pyramid is equal to
`7,133\ cm^(3)`

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

In this problem, the ratio of the height is equal to the scale factor

`z=(4)/(7)`

step 2

Find the volume of the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of the smaller pyramid

y----> volume of the larger pyramid

`z^(3)=(x)/(y)`

we have

`z=(4)/(7)`

`x=1,331\ cm^(3)`

substitute

`((4)/(7))^(3)=(1,331)/(y)\\ \\((64)/(343))=(1,331)/(y)\\ \\y=343*1,331/64\\ \\y=7,133\ cm^(3)`