Question

The volumes of two similar solids are 53 cm^3 and 1113 cm^3, which is the ratio of the corresponding sides?

A) 21
B) 3√21
C) √21
D) 7

Answer 1

The ratio of its corresponding sides is
`\sqrt[3]{21}`

Explanation:

we know that

If two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor. And the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ----> the scale factor

x ----> the volume of the larger solid

y ----> the volume of the smaller solid

so

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

we have

`x=1,113\ cm^(3)`

`y=53\ cm^(3)`

substitute

`z^(3)=(1,113)/(53)=21`

`z=\sqrt[3]{21}`

therefore

The ratio of its corresponding sides is
`\sqrt[3]{21}`