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Surface Area and Volume

Surface Area and Volume

Volume and Density

Volume is a gateway to a lot of other concepts like density, which is a fancy word for the ratio between mass and volume. If something has a high density, then it weighs a lot even if the volume is really small.

A tub of water and a tub of chocolate take up the same amount of space (volume), but the chocolate would weigh more than the water (mass) because of density. It would also be a lot tastier than water, but that has nothing to do with density.

Here's a handy formula to find an object's density, where d is density, M is mass, and V is our old buddy, volume:

d = MV

Pretty simple, right? Just divide the mass by the volume. We can also rearrange it to find mass or volume when we know the other two:

M = dV
= Md

Sample Problem

We have a rectangular carton filled with strawberry Jell-O (after all, strawberry is the best flavor). If strawberry Jell-O weighs 5 pounds per cubic foot, how much does all the Jell-O weigh?

Here's the game plan: We'll find the volume first, multiply by the density, and find the mass that way. Ready? Break!

V = Bh = l × w × h
V = (0.7 ft)(0.8 ft)(1 ft)
V = 0.56 ft3

We have 0.56 ft3 of strawberry Jell-O in the carton. To find the mass, we need to multiply the volume by the density. If we do that, we can see that the cubic feet will cancel each other out and we'll be left with pounds.

M = dV
M = (5 lbs/ft3)(0.56 ft3)
M = 2.8 lbs

Our carton of strawberry Jell-O weighs 2.8 lbs. Bon appétit.

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