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### Course: High school geometry>Unit 9

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
• 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.
• At , what triangles is he talking about
?
• he's talking about the triangles on the cone, basically, he cut a image of a cone into two right similar triangles
• how do you calculate the volume of a tough figure
• will this help me solve the next excercise?
(1 vote)
• can someone tell me why he puts the r on top for the proportion @ ?
why doesn't it go on the bottom?

I figure he's comparing the r to 10 so r:10 or r/10, but I need a deeper understanding as to why ?

Also, trying to conceptiualize if the ratio was 10/r in this problem @ how would the problem , the triangles, the question being asked, and answer differ?

not sure what im missing here, thanks
(1 vote)
• from my proportion I think of it like 10/8=r/6 or 8/10=6/r am I correct in thinking of it this way?

is it always short side over long side when making a proportion for similar triangles ? so if 10 was the radius of the small triangle the 10 would be on top ??
(1 vote)
• Hello, is it possible when calculating the volume of grain inside the cone, to calculate the volume the cone holds in total and multiplying by 6/8 or 3/4 the portion of the cone filled up with grain? It's at that he announces the similar triangle method, I just wanted to know if the method I explained above worked as well.
(1 vote)
• You are partially correct. Similar volumes can be determined through ratio of corresponding edges. However, multiplying by (6 / 8) isn't correct.

Note the following formula (It can be helpful sometimes)

For 2D similar polygon area A_p and A_q with corresponding edges p and q.
``A_p / A_q = (p / q)²``

For 3D similar polyhedral volume V_p and V_q with corresponding edges p and q.
``V_p / V_q = (p / q)³``

Now, lets try using this formula!
Volume of cone = (1 / 3) * 10² * 8 * π = 837.8 m³
Let the volume of grain be V.
V / 837.8 = (6 / 8)³
V = 353.4 m³
(1 vote)