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?

1 Answer
Sep 20, 2017

~~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!