Question

It takes 34 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder with the same base and height as the cone?

I really need help on this ASAP please and thank you

Answer 1

Here, it is helpful to use the formulae for the volume of a cone and a cylinder. I am assuming we are dealing with a right cone and a right cylinder.


`V_(cone)= (1)/(3) \pi r^2h` and
`V_(cyl)= \pi r^2h`.

The volumes of both of these figures are equal to 34 cubic inches, as you said. Notice in our formulae, everything is identical EXCEPT that the volume of a cone is basically that of a cylinder divided by three. To reverse this, that is, to find the volume of the cylinder, we would multiply by 3. 34 cubic inches times 3 is 102 cubic inches.




I would like to add that sometimes these formulae seem totally arbitrary. But when you think about the cylinder like a circle with a rolled-up rectangle, you can see that the
`\pi r^2` part is the area of a circle, and the height is because it's three dimensional. To translate this into the volume of a cone is a bit trickier. It involves calculus...
`\int\ {x^2} \, dx = (1)/(3)x^3`. If that looks like nonsense to you, then you can just remember that a cone is kind of a pointy cylinder and must be smaller than a cylinder!