Question

A side length of solid J is three times the corresponding side length of similar solid K. What is the volume of solid K if the volume of J is 55x cm^3?

Answer 1

`~~2.037cm^3`, if solids J and K are cubical

Explanation:

This answer assumes solids J and K are cubical.

The volume of a cube is `v=l^3`, where `l` is equal to the side length of the cube and `v` is the volume. Therefore, the volume of J is
`55=l^3`. By taking the cube root of boths sides, we get
`root(3)55=l`, or the side length of J is equal to `root(3)55`.

The side length of J is 3 times the side length of K. If we let `L_j` equal the side length of J, and `L_k` the side length of K, we get
`L_j=3L_k`
`root(3)55=3L_k`

`(root(3)55)/3=L_k`, the side length of K.

Going back to our previous work on volume, if the volume of K is equal to the side length of K cubed, we get
`v=(L_k)^3`

`v= (root(3)55)/3 * (root(3)55)/3 * (root(3)55)/3`

`v=55/27` (since `root(n)(a^n)=a`, and `a/b *c/d=(ac)/(bd)`),
`v~~2.037cm^3`
Therefore the volume of K is roughly equal to 2.037 `cm^3`.

I hope I helped!