Tim and Tom are painters. Tim and Tom use a liters of paint on a large shipping crate. If the next crate they need to paint is similar but has three times the volume, how much paint should they plan on buying? Use the given information to provide the desired estimate. If necessary, enter the answer to the nearest hundredth.

Question

Alexis1415 · Answer

Is there by chance a graph, a picture or some sort of representation?

Alexis1415 · Answer

I'm probably guessing there is like a perimeter or a graph of some sort to like explain more thoroughly?

Alexis1415 · Answer

@urmomdotcomisme

Vocaloid · Answer

volume is proportional to the cube of side lengths

V = kx^3

surface area is proportional to the square of side lengths

SA = kx^2

the original crate has volume V, and the volume of the larger crate is 3V (since it has 3 times the volume of the original crate). let's say the sides get scaled up by some constant (let's use c so we don't get it confused with the other constant)

then 3V = k(cx)^3
V = kx^3

divide the two equations to eliminate V and x, then solve for c. that tells you how much each side is scaled up by. now, once you have c, because the surface area is proportional to the square of the side lengths, you can multiply the original surface area by c^2 to get the new surface area. like the problem states, convert to decimal and round to the nearest hundredth (2 decimal places).