Question

For each pair of similar solids, determine the ratio requested.

The ratio of volumes is equal to ? in fraction

Answer 1

A) Ratio of volumes =
`(1)/(25)`

B) Ratio of volumes =
`(343)/(512)`

Explanation:

We have same pair of similar solids , in order to calculate ratio of volumes we divide smaller volume to bigger volume:

A)

Both are cylinders:

Volume of larger cylinder =
`v_1` =
`607.5cm^(3)`

Volume of smaller cylinder =
`v_2` =
`24.3cm^(3)`

∴ Ratio of volumes =
`(v_2)/(v_1)`

⇒ Ratio of volumes =
`(v_2)/(v_1)`

⇒ Ratio of volumes =
`(24.3)/(607.5) = (243)/(6075)`

⇒ Ratio of volumes =
`(1)/(25)`

B)

Both are Prism:

Volume of larger Prism =
`v_1` =
`184.32cm^(3)`

Volume of smaller Prism =
`v_2` =
`123.48cm^(3)`

∴ Ratio of volumes =
`(v_2)/(v_1)`

⇒ Ratio of volumes =
`(v_2)/(v_1)`

⇒ Ratio of volumes =
`(123.48)/(184.32) = (12348)/(18432)`

⇒ Ratio of volumes =
`(343)/(512)`