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## Integrated math 2

### Course: Integrated math 2>Unit 10

Lesson 3: Volume and surface area

# Applying volume of solids

Calculate the volume of a grain hopper and then use the given rate to solve an applied problem. Created by Sal Khan.

## Want to join the conversation?

• Can't we also find the radius of the smaller cone by using the fact that the cones are similar? That is, if they are similar? Instead of taking a cross section and proving that the triangles in the cross section are similar... Is there any situation where this won't work?
• Sal does that at when he sets up the equation r/10=6/8 to find r= 7.5. Since it is a single cone, each measure will be proportional
• Just think of Minecraft hoppers if you can't think of what a hopper is.
• Good example! :)
• when u have a can of beans and the height is 11 and the rades is 12 what will be an answer. my mom really needs to know because we r going to be using some beans tonight with dinner. yummmmmmmmmmmmmmy. also we r having hot dog wennies but I will save that problem for later.
• What can of beans has a diameter that is more than twice the height? V=πr^2 h
• At about in the video, Sal multiplies 6 by 1/3. Wouldn't he have to do the same for the 7.5? Why doesn't he?

At , he says that dividing by 1/10 is the same as multiplying by 10. How is this possible? Also, why does he multiply by 10?
(1 vote)
• Multiplication is commutative, so we can move things around to make it easy to multiply. So 1/3*(7.5)^2*6 can be commuted to (7.5)^2 * 1/3 * 6. You are trying to apply the distributive property which is not the same, you are trying to do 1/3((7.5)^2 + 6) where both terms would be multiplied by 1/3, but the problem has a single term.
As to the second issue, dividing by a tenth can be shown in two ways, 353.4/.1, multiplying both numerator and denominator by 10 (10/10=1) gives 3534/1, and dividing by 1 does not change a number, so it is not needed. The second way is 353.4/(1/10). To divide a whole number by a fraction, we reciprocate the fraction and multiply which gives 353.4*(10/1)=3534.