Question
Find the volume of corn held in this cone-shaped grain silo. Use 3.14 for π and round to the nearest cubic foot.
- About 301 ft3
- About 302 ft3
- About 376 ft3
- About 377 ft3
Hint:
When it comes to mensuration one can find an expression for volume of a structure and then calculate necessary attributes from the given attributes of a structure.
The correct answer is: About 301 ft3
Given that:
Slant height of a cone (l) = 10 feet
Radius of a cone (r) = 5 feet
Hence, volume of a cone is =
=
=
= 301.44 feet3.
Hence, Volume of a cone is 301.44 ~ 301 cubic feet.
As we know volume of the cone is Base area Height .
Area of the base circle = r2
Hence, volume of the cone = r2h
From the above figure:
Using Pythagoras theorem: (AC)2 = (AB)2 + (BC)2.
>>> l2 = h2 + r2
Hence, height (h) =
Similarly we can find radius with height and slant height.
Hence, the volume of a cone becomes :
Since, we have derived an expression for volume of a cone as . hence, substituting the values of radius and slant height values we can obtain volume of a cone easily.
Related Questions to study
A cone has the radius of 5.5 inches and the height of 12 inches. Find the volume of the cone. Round your answer to the nearest tenth.
Since, we have derived the volume of the cone as r2h. Then, just substitute the given values and find the volume of the cone.
Given Data:
Radius of the cone = 5.5 inches
Height of the cone = 12 inches
Hence, Volume of the Cone = r2h
=
=379.64
***Volume of the cone is 379.64.. ~ 380.13 inches3.
A cone has the radius of 5.5 inches and the height of 12 inches. Find the volume of the cone. Round your answer to the nearest tenth.
Since, we have derived the volume of the cone as r2h. Then, just substitute the given values and find the volume of the cone.
Given Data:
Radius of the cone = 5.5 inches
Height of the cone = 12 inches
Hence, Volume of the Cone = r2h
=
=379.64
***Volume of the cone is 379.64.. ~ 380.13 inches3.
Calculate the volume of a cone with a diameter of 30 feet and a height of 60 feet. Use 3.14 for π.
Since, we have derived the volume of the cone it is easy to find the volume from the given data.
Given That:
Diameter of a base of a cone = 30 feet
we know that 2Radius=Diameter then,
Radius of a base of a cone =15 feet
Height of a cone = 60 feet
From the volume of the cone = r2h
=
=14130 feet3
***Hence, the volume of a cone is 14130 cubic feet.
Calculate the volume of a cone with a diameter of 30 feet and a height of 60 feet. Use 3.14 for π.
Since, we have derived the volume of the cone it is easy to find the volume from the given data.
Given That:
Diameter of a base of a cone = 30 feet
we know that 2Radius=Diameter then,
Radius of a base of a cone =15 feet
Height of a cone = 60 feet
From the volume of the cone = r2h
=
=14130 feet3
***Hence, the volume of a cone is 14130 cubic feet.
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.
Since, we have derived the volume of a cone as r2h.
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).
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.
Since, we have derived the volume of a cone as r2h.
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).
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.