Calculate Volume of a Cone: Formulas & Steps

[Ruturaj Vaidya]

The required Formulas are:

Area of circle = Pi (r)^2

Volume of Cone = 1/3 Pi (r)^2 h

Here is my try:

I know the smaller cone and bigger ones are congurent, so

50/25 = 15/h

h=7.5, but the answer is incorrect. Please help

 

[pbuk]

50/25 = 15/h

This is not correct: the height of the bigger cone is not 15.

 

[Ruturaj Vaidya]

Yes, thanks, I have realized that . The total height is 30m. However, I can't calculate the volume of fiber composite needed?

 

[Mark44]

Yes, thanks, I have realized that . The total height is 30m. However, I can't calculate the volume of fiber composite needed?

You need the formula for the volume of a frustum of a cone. Find the volume of the outer portion of the cone, and then find the volume of the inside, which is also a frustum of a cone, but a little bit smaller.

 

[Ruturaj Vaidya]

Yes, I have tried that, but that does not work either :(

 

[Mark44]

Yes, I have tried that, but that does not work either :(

Why do you think it doesn't work. Please show us what you did.

 

[Ruturaj Vaidya]

Here is what I did:

I found that the net of the cone are basically two rings (for the composite fiber) and a trapezium)for the curved surface.
It is a three dimensional trapezium, so I multiplied the trapezium's area by the width (2.5cm). I subtracted the volume of the larger trapezium prism with that of the smaller trapezium prism, to gain the composite fiber volume. Here is my working:

However, the answer is ridiculously large, and even when I don't add the area of the circles (as seen above), the answer remains large. The solutions sheet says that the answer is closer to 8.67 cm^3

 

[SteamKing]

You have the height of a cone measured in meters.
You have the diameter of the cone measured in centimeters.
You have the thickness of the composite measured in millimeters.

So naturally, you just throw all of these different units into a giant crank and expect volume in cubic centimeters to emerge automatically.

IDK what you are doing using the formula for volume of a three dimensional trapeze-whatever.

This problem can be solved knowing the formula for the volume of a cone and only that formula.

 

[Mark44]

Here is what I did:

I found that the net of the cone are basically two rings (for the composite fiber) and a trapezium)for the curved surface.
It is a three dimensional trapezium, so I multiplied the trapezium's area by the width (2.5cm). I subtracted the volume of the larger trapezium prism with that of the smaller trapezium prism, to gain the composite fiber volume. Here is my workingowever, the answer is ridiculously large, and even when I don't add the area of the circles (as seen above), the answer remains large. The solutions sheet says that the answer is closer to 8.67 cm^3

You really have things confused here. The image you showed has a trapezoidal shaped solid that has nothing to do with this problem, and you mentioned "area of circles" above.