# Help with ratio of volume of similar solids.

• Jan 27th 2013, 05:54 AM
Aroperalta
Help with ratio of volume of similar solids.
A wooden cone is cut into 3 parts, A,B and C by 2 planes parallel to the base. The height of the 3 parts are equal.find
i. The ratio of volume of a,b,c
ii. The ratio of the base area of part a,b,c

Please show the working. Really have no clue on how to do it.
i could draw the diagram but i have no idea how to get the answs
• Jan 27th 2013, 05:57 AM
Prove It
Re: Help with ratio of volume of similar solids.
Am I correct in assuming that since you want the figures to be similar, you're not cutting the cone into three parts (which would give a single cone and two frustrums), you're creating three cones, correct?
• Jan 27th 2013, 06:04 AM
Aroperalta
Re: Help with ratio of volume of similar solids.
Nope. Its like this:
/\
/--\
/----\
/____\.
So basically 1 cone on top. 2 trapizuim of different
Size. But the height of the a:cone b:small trapizuim
c: big trapizuim are the same.
• Jan 27th 2013, 06:06 AM
Aroperalta
Re: Help with ratio of volume of similar solids.
..no given numbers
• Jan 29th 2013, 08:34 PM
bjhopper
Re: Help with ratio of volume of similar solids.
Hi aroperalta,
You don;t need given numbers because you are looking for relative volumes.The top cone has a v1 = 1/3pi r^2h.The next cone V2 -1/3 (2r)^2*2h. The third cone V3=1/3pi (3r)^2*3h.Differences between them defines the trapezoid like volumes.When you write the difference equations you will see that Va,Vb,Vc are related by relative volume numbers
• Jan 29th 2013, 09:51 PM
Prove It
Re: Help with ratio of volume of similar solids.
Quote:

Originally Posted by bjhopper
Hi aroperalta,
You don;t need given numbers because you are looking for relative volumes.The top cone has a v1 = 1/3pi r^2h.The next cone V2 -1/3 (2r)^2*2h. The third cone V3=1/3pi (3r)^2*3h.Differences between them defines the trapezoid like volumes.When you write the difference equations you will see that Va,Vb,Vc are related by relative volume numbers

No, that is incorrect. You need to remember that when a length (such as the height) is scaled, then the volume is scaled by the CUBE of that scaling factor.

So that means that the top cone would be \displaystyle \begin{align*} \left( \frac{1}{3} \right)^3 V \end{align*}, etc..., where V is the original volume of the cone.
• Jan 30th 2013, 05:00 AM
bjhopper
Re: Help with ratio of volume of similar solids.
Quote:

Originally Posted by Prove It
No, that is incorrect. You need to remember that when a length (such as the height) is scaled, then the volume is scaled by the CUBE of that scaling factor.

So that means that the top cone would be \displaystyle \begin{align*} \left( \frac{1}{3} \right)^3 V \end{align*}, etc..., where V is the original volume of the cone.

The volume of a cone = 1/3pi r^2h r^2h is a cubic measure