1,562 views
27 votes
27 votes
A cube is dilated by a factor of 3.5.The volume of the resulting cube is ___ times the volume of the original cube.

User Joebobfrank
by
2.4k points

1 Answer

24 votes
24 votes

A volume of a cube is given by V=L^3 where L is its side length. If a cube is dilated by a factor of 3.5, it means that its sidelength is increased by a factor of 3.5, i.e. if S is the first length, the new length L satisfies L=3.5*S. Now, the old cube's volume v was v=S^3, after it has expanded to the new sidelength L its new volume V is V=L^3. Using the equation L=3.5*S we can replace L in the equation for V like follows:

V=(3.5*S)^3

Expanding the product we get

V=[(3.5)^3]*(S^3)=42.875*(S^3)

We previously noticed that the prior volume of the cube was v=S^3. Replacing v for S^3 in the previeus equation gives us:

V=42.875v

Thus, the factor by wich the volume of the original cube was scaled up is 42.875

User SrPanda
by
3.0k points