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Q: How to find the volume of a cylinder with a cone at the top?

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To find the answer to this question you would have to know how to find the volume of a cone. First, find the angle of the side to the base to determine at what height a cone would be formed if the sides of the cylinder extended all the way up to a single point. This would be the height of the cone. Take this number and put into the equation Assuming you know the radius of the cylinder at the bottom, the wider side. Next, subtract the total height of the cone from the height of the cylinder you want to know the volume of. You will now be finding the volume of the smaller cone within the larger cone. Put the smaller height into the above equation now using the radius of the top part of cylinder. Subtract this total from the total volume of the biggest cone and you will have the volume of a cylinder that is smaller on one end.

The volume is 3500000/3 π mm3 ~=3665191 mm3 (~= 3.67 litres). A cylinder normally has a constant cross section. What you have is a cone with the top chopped off, thus its volume is the volume of the whole cone minus the volume of the top cone: The diameter reduces from 200mm to 100mm (that is 100mm) in 200mm height so it will reduce from 100mm to 0mm (that is a further 100mm) in a further 200mm height. So the "whole" cone has a height of 200mm+200mm = 400mm and the "top" cone has a height of 200mm. The volume of a cone is 1/3πr2h, so the volume of the "cylinder" is: volume = volume_whole_cone - volume_top_cone = 1/3π(200 ÷ 2)2400 mm3 - 1/3π(100 ÷ 2)2200 mm3 = 200/3π(1002x2 - 502) mm3 = 3500000/3 π mm3 ~= 3665191 mm3 ~= 3665 cm3 = 3.665 litres.

A cone on top of a cylinder.

because on the top their circles

I believe it is a cone

VariablesD = Cylinder diameter [L].Dbot = Cone bottom diameter [L].Dtop = Cone top diameter [L].h = Cone height [L].L = Cylinder length [L].T = Top width of liquid in cylinder [L].y = Liquid depth in sphere or cylinder [L].z = Horizontal to vertical side slope of cone. zDbot.Ø = Angle representing how full the cylinder is [radians or degrees]. An empty cylinder has Ø=0o, a cylinder with Ø=180o is half full, and a cylinder with Ø=360o is completely full.

No, it is a cylinder. The top few inches, might be seen as a cone.

Take the base Radius to be R1, the top radius to be R2. Then the volume for the "cone" is V = Pi * (R12 + R1R2 + R22) * Height / 3

because the flat side of a cone is a circle.

An apex is where the sides of a triangle or cone meet at the top to form a point therefore a cylinder does not have an apex.

No, it is not. For a cone, think of a standard ice-cream cone shape (or a witches hat) - a circular top OR base (but not both), which has sides coming off that taper into a point. Whereas a cylinder has a circular top AND base, (like the shape of baked bean cans), with sides joining both top and base.

It's a frustum! to find the area of this figure you need to take the area of the entire cone and subtract the area of the mini cone. Let me explain.If you keep extending thesideofthe figure into the direction of the smaller circle, it creates a cone, right? so take volume (1/3 area of base * height) of the entire extended cone (whose base is the bigger circle to the vertex). Then take the volume of the top cone(whose base is the small circle to the vertex). Subtract the small one from the big one, and it gives you the area of the frustum.

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