Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimension of common geometric shapes (prisms, cylinders, cones, and spheres) will affect the volume of these shapes.

Question

mjdennis · Answer

Pick a shape that you know the formula for, or can find a formula you understand

jim_thompson5910 · Answer

This problem seems similar to yours. Hopefully it helps you point in the right direction. http://openstudy.com/study#/updates/57407449e4b04179a4191f83

jim_thompson5910 · Answer

In that link, the volume is held to 288 cubic inches and isn't allowed to be changed. The surface areas change though.

jim_thompson5910 · Answer

This chart of formulas also may be handy http://schooltutoring.com/wp-content/uploads/sites/2/2012/04/volume1.png

simplymarie_x · Answer

We can do the cone formula so V=1/3πr^2 @mjdennis

jim_thompson5910 · Answer

don't forget about the height h

simplymarie_x · Answer

oh i deleted that accidentally bc i did /3 but changed it to 1/3

jim_thompson5910 · Answer

ah that makes sense

simplymarie_x · Answer

So v = 1/3πr^2h

jim_thompson5910 · Answer

yes

simplymarie_x · Answer

So like, what do I do after? I read that link but I don't get it :/

jim_thompson5910 · Answer

ok let's say we start with a box that is 2x5x10 inches

what is the volume of this box?

formula
V = L*W*H

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

100 cubic inches, yes

simplymarie_x · Answer

oh oops deleted my comment aha but oh okay (-:

jim_thompson5910 · Answer

if we made the base of 2 turn into 5, then we'd have 

5*5*10 = 250 cubic inches

of volume

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jim_thompson5910 · Answer

now imagine us putting a cylinder in the box. Think of the box as a shipping box and the cylinder as some product (maybe a bottle of shampoo or something)

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jim_thompson5910 · Answer

it's badly drawn, but the cylinder would have a radius of 5/2 = 2.5 inches

the height of the cylinder is 10 inches

what is the volume of this cylinder?

simplymarie_x · Answer

196.35?

jim_thompson5910 · Answer

yes

jim_thompson5910 · Answer

the 5x5x10 box has a volume of 250 cubic inches
the cylinder inside the same box has a volume of 196.35 cubic inches (this is approximate)

so as you'd expect, the cylinder that its in the box has a smaller volume so it fits inside. There's empty space not being used

jim_thompson5910 · Answer

If we place a cone inside the cylinder, then the cone will have the same base but 1/3 of the volume of the cylinder
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