Question
A cone has the radius of 2 cm and the height of 3 cm. Calculate the volume of the cone. Round your answer to the nearest tenth.
- 820.25 cm3
- 12 cm3
- 883.13 cm3
- 12.57 cm3
Hint:
When it comes to mensuration one can find attributes of a structures through any relevant methods offered. Anyhow, once one has obtained an expression for the volume of any structure, just substitute to obtain any variable attribute.
The correct answer is: 12.57 cm3
Given that:
Radius of a base of a cone : 2 cm
Height of a cone : 3 cm
Hence, Volume of a cone = 
r2h
= 
=12.571428 cubic cm.
* it may vary by taking different 
values(3.14 for now).
**** Hence, the volume of a cone is 12.57(rounding off to it's nearest tenth).
Cone is a 3-Dimensional Geometric Structure which is associated by a circle and whose end points of a diameter is connected at a point called apex or cone vertex. Since, it is a closed structure it has a property of having volume. Since, it is a derived structure from Cylinder the volume of cone depends on the volume of a cylinder.
Hence, if we obtain volume of a cylinder, it is simple task to evaluate an expression for a volume of a cone.
Volume of any Structure = Base area 
Height
Similarly, The volume of a Cylinder = Area of base circle Height of a cylinder
= r2h
where, r is the radius of the base circle and h be the height of a Cylinder.
***Hence, we know that Volume of a cone =1/3(Volume of a Cylinder)
=r2h
Hence, we obtained the required volume of a cone = r2h
Related Questions to study
A cone has the radius of 10 cm and the height of 8 cm. Find the volume of the cone. Round your answer to the nearest tenth.
Hence, We have derived an expression for an volume of the cone as r2h.
Given that:
radius of the base of a cone: 10 cm
height of a cone : 8 cm
Hence, Volume of a cone= r2h.
=
= 837.334 cubic cm
*** Volume of the con is 837.334 cubic cm.
* It may vary based on the value of taken.(In general =3.14)
A cone has the radius of 10 cm and the height of 8 cm. Find the volume of the cone. Round your answer to the nearest tenth.
Hence, We have derived an expression for an volume of the cone as r2h.
Given that:
radius of the base of a cone: 10 cm
height of a cone : 8 cm
Hence, Volume of a cone= r2h.
=
= 837.334 cubic cm
*** Volume of the con is 837.334 cubic cm.
* It may vary based on the value of taken.(In general =3.14)
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?
Since, We have derived volume of a cone as 
r2h.
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.
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?
Since, We have derived volume of a cone as r2h.
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.
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.
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.
