Question

20 POINTS! Two similar solids have heights of 6 cm and 9 cm. If the volume of the smaller solid is 88 cm^3, calculate the volume of the larger solid.

PLEASE give an explanation with your answer! PLEASE!​

Answer 1

Answer:
`132cm^(3)`

Step-by-step explanation:

The volume
`V` of a solid is given by the multiplication of its three dimensions:

`V=(height)(widgth)(length)`

In this case we have two similar solids with volumes
`V_(1)=88cm^(3)` and
`V_(2)`, and we only have information about the height of each solid
`h_(1)=6cm` and
`h_(2)=9cm`.

Now, there is a theorem for similar solids, which establishes the ratio of their volume is
`(V_(1))/(V_(2))` and the ratio of one of their corresponding sides (the height in this case) is
`(h_(1))/(h_(2))`.

Knowing this, we can write the following relation:

`(V_(1))/(V_(2))=(h_(1))/(h_(2))`

Substituting the known values:

`(88cm^(3))/(V_(2))=(6cm)/(9cm)`

Fially finding
`V_(2)`:

`V_(2)=132cm^(3)`