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: $132cm^{3}$

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 $\frac{V_{1}}{V_{2}}$ and the ratio of one of their corresponding sides (the height in this case) is $\frac{h_{1}}{h_{2}}$.

Knowing this, we can write the following relation:

$\frac{V_{1}}{V_{2}}=\frac{h_{1}}{h_{2}}$

Substituting the known values:

$\frac{88cm^{3}}{V_{2}}=\frac{6cm}{9cm}$

Fially finding $V_{2}$:

$V_{2}=132cm^{3}$