Mathematics
Grade-8
Easy

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.

  1.  About 301 ft3
  2.  About 302 ft3
  3.  About 376 ft3
  4.  About 377 ft3

hintHint:

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 =   1 third πr to the power of 2 to the power of blank end exponentsquare root of l squared space minus space r squared end root
    =fraction numerator 3.14 cross times 6 cross times 6 cross times square root of 100 minus 36 end root over denominator 3 end fraction
    =fraction numerator 3.14 cross times 6 cross times 6 cross times 8 over denominator 3 end fraction
    = 301.44 feet3.
    Hence, Volume of a cone is 301.44 ~ 301 cubic feet.


    As we know volume of the cone is 1 third cross timesBase area cross times Height .
    Area of the base circle = straight pir2

    Hence, volume of the cone = 1 thirdstraight pir2h

    From the above figure:
    Using Pythagoras theorem: (AC)2 = (AB)2 + (BC)2.
    >>> l2 = h2 + r2
    Hence, height (h) = square root of l squared space minus space r squared end root
    Similarly we can find radius with height and slant height.
    Hence, the volume of a cone becomes : 1 third πr to the power of 2 to the power of blank end exponentsquare root of l squared space minus space r squared end root
    Since, we have derived an expression for volume of a cone as  1 third πr to the power of 2 to the power of blank end exponentsquare root of l squared space minus space r squared end root. hence, substituting the values of radius and slant height values we can obtain volume of a cone easily.

    Related Questions to study

    Grade-8
    Mathematics

    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 1 third straight pir2h. 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 = 1 thirdstraight pir2h
    =fraction numerator 3.14 cross times 5.5 cross times 5.5 cross times 12 over denominator 3 end fraction
    =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.

    MathematicsGrade-8

    Since, we have derived the volume of the cone as 1 third straight pir2h. 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 = 1 thirdstraight pir2h
    =fraction numerator 3.14 cross times 5.5 cross times 5.5 cross times 12 over denominator 3 end fraction
    =379.64
    ***Volume of the cone is 379.64.. ~ 380.13 inches3.

    Grade-8
    Mathematics

    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 2cross timesRadius=Diameter then,
    Radius of a base of a cone =15 feet
    Height of a cone = 60 feet
    From the volume of the cone = 1 third straight pir2h
    =fraction numerator 3.14 cross times 15 cross times 15 cross times 60 over denominator 3 end fraction
    =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.

    MathematicsGrade-8

    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 2cross timesRadius=Diameter then,
    Radius of a base of a cone =15 feet
    Height of a cone = 60 feet
    From the volume of the cone = 1 third straight pir2h
    =fraction numerator 3.14 cross times 15 cross times 15 cross times 60 over denominator 3 end fraction
    =14130 feet3

    ***Hence, the volume of a cone is 14130 cubic feet.

    Grade-8
    Mathematics

    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 1 thirdstraight pir2h.
    Given that:
    Radius of a base of a cone : 2 cm
    Height of a cone : 3 cm
    Hence, Volume of a cone = 1 third straight pir2h
    fraction numerator 22 cross times 2 cross times 2 cross times 3 over denominator 7 cross times 3 end fraction
    =12.571428 cubic cm.
    * it may vary by taking different straight pi 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.

    MathematicsGrade-8

    Since, we have derived the volume of a cone as 1 thirdstraight pir2h.
    Given that:
    Radius of a base of a cone : 2 cm
    Height of a cone : 3 cm
    Hence, Volume of a cone = 1 third straight pir2h
    fraction numerator 22 cross times 2 cross times 2 cross times 3 over denominator 7 cross times 3 end fraction
    =12.571428 cubic cm.
    * it may vary by taking different straight pi values(3.14 for now).
    **** Hence, the volume of a cone is 12.57(rounding off to it's nearest tenth).

    parallel
    Grade-8
    Mathematics

    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 1 third straight pir2h.
    Given that:
    radius of the base of a cone: 10 cm
    height of a cone : 8 cm
    Hence, Volume of a cone= 1 third straight pir2h.
    =fraction numerator 3.14 cross times 10 cross times 10 cross times 8 over denominator 3 end fraction
    = 837.334 cubic cm
    *** Volume of the con is 837.334 cubic cm.
    * It may vary based on the value of straight pi taken.(In general straight pi=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.

    MathematicsGrade-8

    Hence, We have derived an expression for an volume of the cone as 1 third straight pir2h.
    Given that:
    radius of the base of a cone: 10 cm
    height of a cone : 8 cm
    Hence, Volume of a cone= 1 third straight pir2h.
    =fraction numerator 3.14 cross times 10 cross times 10 cross times 8 over denominator 3 end fraction
    = 837.334 cubic cm
    *** Volume of the con is 837.334 cubic cm.
    * It may vary based on the value of straight pi taken.(In general straight pi=3.14)

    Grade-8
    Mathematics

    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 1 thirdstraight pir2h.
    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=fraction numerator 3 cross times V over denominator straight pi cross times straight r cross times straight r end fraction
    Height = fraction numerator 3 cross times 314 over denominator 3.14 cross times 5 cross times 5 end fraction
    = 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?

    MathematicsGrade-8

    Since, We have derived volume of a cone as 1 thirdstraight pir2h.
    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=fraction numerator 3 cross times V over denominator straight pi cross times straight r cross times straight r end fraction
    Height = fraction numerator 3 cross times 314 over denominator 3.14 cross times 5 cross times 5 end fraction
    = 12 inches
    *** Height of a cone is 12 inches.

    Grade-8
    Mathematics

    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 1 thirdstraight pir2h.
    Given That:
    Height of the Cone (h) = 4 inches
    Diameter of the Base = 8 inches
    We know in any Circle:
    2cross timesRadius=Diameter
    Then, Radius=4 inches.
    Hence, Base area = 1 thirdstraight pir2
    =1 third cross times3.14cross times16
    = 16.7467
    Hence, The volume of a cone = Base Area cross times Height
    =16.7467cross times4
    =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.

    MathematicsGrade-8

    Hence, We have derived the volume of a cone that is 1 thirdstraight pir2h.
    Given That:
    Height of the Cone (h) = 4 inches
    Diameter of the Base = 8 inches
    We know in any Circle:
    2cross timesRadius=Diameter
    Then, Radius=4 inches.
    Hence, Base area = 1 thirdstraight pir2
    =1 third cross times3.14cross times16
    = 16.7467
    Hence, The volume of a cone = Base Area cross times Height
    =16.7467cross times4
    =66.9868 ~67.02
    Volume of Cone is 67.02 cubic inches.

    parallel
    Grade-8
    Mathematics

    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 : straight pir2h
    Similarly, Volume of the Cone is: 1 thirdstraight pir2h.
    ***Volume of a Cone = 1 thirdcross timesVolume of a Cylinder.
    ***Volume of a Cylinder = 3cross times 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?

    MathematicsGrade-8


    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 : straight pir2h
    Similarly, Volume of the Cone is: 1 thirdstraight pir2h.
    ***Volume of a Cone = 1 thirdcross timesVolume of a Cylinder.
    ***Volume of a Cylinder = 3cross times Volume of Cone.
    Hence, We can say that Volume of the Cylinder is Three times the volume of the Cone.

    Grade-8
    Mathematics

    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 2cross timesradius=diameter. Then. radius=4 feet.
    height of a cone = 3 feet.
    Hence, Volume of a cone = 1 thirdcross times Area of a circular base cross times Height
    Area of a circular base: straight pir2 = 3.14cross times 42 = 50.24 ft2 .
    Volume of Cone = 1 third cross times50.24cross times3 = 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.

    MathematicsGrade-8

    The Given Data:
    Diameter of a circular base: 8 feet
    We know 2cross timesradius=diameter. Then. radius=4 feet.
    height of a cone = 3 feet.
    Hence, Volume of a cone = 1 thirdcross times Area of a circular base cross times Height
    Area of a circular base: straight pir2 = 3.14cross times 42 = 50.24 ft2 .
    Volume of Cone = 1 third cross times50.24cross times3 = 50.24 ft3.
    Hence, The volume of a cone is equal to the 50.24 cubic feet.

    Grade-8
    Mathematics

    A cone has the radius of 7.5 cm and the height of 5 cm. The volume of the cone rounded to the nearest tenth is ____________.

    A cone has the radius of 7.5 cm and the height of 5 cm. The volume of the cone rounded to the nearest tenth is ____________.

    MathematicsGrade-8
    parallel
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    A party hat has a volume of 75straight pi cubic inches. If the radius is 5 inches, what is the height of the party hat?

    A party hat has a volume of 75straight pi cubic inches. If the radius is 5 inches, what is the height of the party hat?

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    Find the volume of the cone. (Round to the nearest integer.)

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    The formula for Volume of a Cone is,

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