Question
A cone and a cylinder have the same diameter and height. How many times greater is the cylinder's volume than the cone's?
- 1
- 2
- 3
- 4
Hint:
We can find volume of any shape through general formula explorer or through Integration of one small part in order to find the total volume of the shape. Find the volume and relate between them.
The correct answer is: 3
Since, We know the volume of a cylinder and volume of a cone, we can easily relate between them.
As, we seen before Volume of a Cylinder is given by : 
r2h
Similarly, Volume of the Cone is: 
r2h.
***Volume of a Cone = 
Volume of a Cylinder.
***Volume of a Cylinder = 3 Volume of Cone.
Hence, We can say that Volume of the Cylinder is Three times the volume of the Cone.
***Cylinder is 3-Dimensional Geometric Shape that has two circles with long narrow area in between the circles. Since cylinder has 2 circles it's area becomes much bigger than other models. Hence, We know that Volume of any shape or model is labelled as product of area of a base to the height of a model.
Volume of a Model = Base Area Height of Model.
Since, Cylinder has circle as a base. Area of a circle is given by 
r2 and let h be the height of a cylinder.
Then, Volume of a cylinder is: r2h = r2h.
***Cone is a 3-Dimensional Geometric shape that has one circle as a base and end points of a diameter is connected at point called as apex point or cone vertex.
Since, Cone doesn't cover entire volume as we seen in cylinder. It's 1/3 portion is filled since, it is joined from end points of a diameter at one point.
Hence, The Volume of a Cone is: r2h.
Related Questions to study
Mike created a cone that has a diameter of 8 feet and a height of 3 feet. Find the volume of this cone.
The Given Data:
Diameter of a circular base: 8 feet
We know 2radius=diameter. Then. radius=4 feet.
height of a cone = 3 feet.
Hence, Volume of a cone = Area of a circular base Height
Area of a circular base: r2 = 3.14 42 = 50.24 ft2 .
Volume of Cone = 
50.243 = 50.24 ft3.
Hence, The volume of a cone is equal to the 50.24 cubic feet.
Mike created a cone that has a diameter of 8 feet and a height of 3 feet. Find the volume of this cone.
The Given Data:
Diameter of a circular base: 8 feet
We know 2radius=diameter. Then. radius=4 feet.
height of a cone = 3 feet.
Hence, Volume of a cone = Area of a circular base Height
Area of a circular base: r2 = 3.14 42 = 50.24 ft2 .
Volume of Cone = 50.243 = 50.24 ft3.
Hence, The volume of a cone is equal to the 50.24 cubic feet.
