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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Could somebody please help me with this geometry question?

This is one of the questions for an assignment for geometry. The thing is, the lesson did not cover how to combine equations into one. The one I picked may be wrong, but could someone explain this to me please? 

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  • 2 months ago

    The equation for the volume of a cylinder is:

    V = πr²h

    The equation for the volume of a cone is:

    V = πr²h / 3

    If the height of the cylinder is 3 times the height of the cone, then our equations come to:

    V = πr²(3h) and V = πr²h / 3

    The total volume is the sum of the two expressions:

    πr²(3h) + πr²h / 3

    Simplify the first term:

    3πr²h + πr²h / 3

    Common denominator:

    9πr²h / 3 + πr²h / 3

    Add the numerators:

    (9πr²h + πr²h) / 3

    And simplify:

    10πr²h / 3

    which can also be written as:

    (10/3)πr²h

    Which is answer B.

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  • 2 months ago

    volume of cylinder = πr²h

    Cone volume V = ⅓πr²h, h is height of cone (not slant)

    in this case

    volume of cylinder = πr²3h

    volume of cone = ⅓πr²h

    add the two

    total volume = 3πr²h + ⅓πr²h

    total volume = (9/3)πr²h + ⅓πr²h = (10/3)πr²h

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  • 2 months ago

    the cone and the cylinder both have the same radius

    - this is clear in the picture, r for the cylinder = r for the cone

    the height of the cylinder is 3 times the height of the cone

    - this is also clear in the picture, the height of the cone is h, the height of the cylinder is 3h

    finding the total volume

    Total volume = volume of cone + volume of cylinder

    volume of cone = 1/3 pi Rcone-squared Hcone

    volume of cylinder = pi Rcylinder-squared Hcylinder

    Rcone = Rcylinder = r

    Hcone = h

    Hcylinder = 3h

    plugging those values into the previous equations, we get

    volume of cone = 1/3 pi r-squared h

    volume of cylinder = pi r-squared 3h = 3 pi r-squared h

    total volume = 1/3 [pi r-squared h] + 3 [pi r-squared h]

    = 3+1/3 [pi r-squared h]

    = 10/3 [pi r-squared h]

    = 10/3 pi r-squared h

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  • 2 months ago

    Most people take algebra before geometry.  You are not combing equations.  You are adding volumes.  The volume of the cylinder is 3(pi)(r^2)h.  The cone is (1/3)(pi)r^2)h. The total is 3(pi)(r^2)h + (1/3)(pi)r^2)h = (3+ 1/3)(pi)(r^2)h by the distributive law. 3+1/3 = 10/3. 

    • Keith A
      Lv 6
      2 months agoReport

      Oops! For the cylinder, (just) pi * r^2 * h.

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