Question
A cone with a radius of 5 inches has a volume of approximately 314 cubic inches. Which of the following best represents the height of the cone?
- 8 inches
- 4 inches
- 12 inches
- 16 inches
Hint:
Volume of a cone is generally calculated in various methods. One of the finest method is general formula explorer and second major option is using Integration. Anyhow if one obtain an expression for the volume then, substitute and derive any unorder variables.
The correct answer is: 12 inches
Given that:
Radius of base = 5 inches
Volume of a cone = 314 cubic inches
*** From the formula of volume of a cone that we derived, height of a cone h can be retrieved as
h=
Height = 
= 12 inches
*** Height of a cone is 12 inches.
Cone is 3-Dimensional Geometric structure which is associated with one circle as a base and its endpoints of a diameter is connected at one point called apex or cone vertex. Hence, we can say that it is a derived structure from cylinder. Hence, If you find volume of a cylinder we can find volume of a cone easily.
Volume of Cylinder is defined as a product of base area and the height of a cylinder. since circle is the base base area becomes 
r2 let h be the height of the cylinder. Hence, Volume of a cylinder= r2h.
We know the volume of the cone is 1/3 portion of the volume of the cylinder. Hence, The volume of a cone =
r2h.
***Volume of the Cone = r2h
Since, We have derived volume of a cone as 
r2h.
Related Questions to study
An ice cream cone that is 4 inches tall has an opening that is 8 inches across. Find the volume of the cone.
Hence, We have derived the volume of a cone that is r2h.
Given That:
Height of the Cone (h) = 4 inches
Diameter of the Base = 8 inches
We know in any Circle:
2
Radius=Diameter
Then, Radius=4 inches.
Hence, Base area = r2
=3.1416
= 16.7467
Hence, The volume of a cone = Base Area Height
=16.74674
=66.9868 ~67.02
Volume of Cone is 67.02 cubic inches.
An ice cream cone that is 4 inches tall has an opening that is 8 inches across. Find the volume of the cone.
Hence, We have derived the volume of a cone that is r2h.
Given That:
Height of the Cone (h) = 4 inches
Diameter of the Base = 8 inches
We know in any Circle:
2Radius=Diameter
Then, Radius=4 inches.
Hence, Base area = r2
=3.1416
= 16.7467
Hence, The volume of a cone = Base Area Height
=16.74674
=66.9868 ~67.02
Volume of Cone is 67.02 cubic inches.
A cone and a cylinder have the same diameter and height. How many times greater is the cylinder's volume than the cone's?
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.
A cone and a cylinder have the same diameter and height. How many times greater is the cylinder's volume than the cone's?
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.
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.
