Mathematics

Question

cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.

Use pi = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

2 Answer

  • Answer:

    [tex]V_{cylinder}=251.2\ in^3,[/tex]

    [tex]V_{cone}=251.2\ in^3,[/tex]

    [tex]V_{cylinder}=V_{cone}.[/tex]

    Step-by-step explanation:

    The volume of the cylinder is

    [tex]V_{cylinder}=\pi r^2 h,[/tex]

    where r is the radius of a base circle and h is the cylinder's height.

    If cylinder has diameter of 8 inches, then its radius is 4 inches. The height of the cylinder is 5 inches. Thus, the volume of the cylinder is

    [tex]V_{cylinder}=3.14\cdot 4^2\cdot 5=251.2\ in^3.[/tex]

    The volume of the cone is

    [tex]V_{cone}=\dfrac{1}{3}\pi r^2 h,[/tex]

    where r is the radius of a base circle and h is the cone's height.

    If cone has diameter of 8 inches, then its radius is 4 inches. The height of the cone is 15 inches. Thus, the volume of the cone is

    [tex]V_{cylinder}=\dfrac{1}{3}\cdot 3.14\cdot 4^2\cdot 15=251.2\ in^3.[/tex]

    As you can see the cylinder and the cone have the same volume.

  • COOL PEOPLE COOL ANSWERS AND COOL ANSWERS ARE ALWAYS CORRECT SO CHECK THIS OUT!!!! NO DELETING ANSWERS

    Step-by-step explanation:

    pi r2h  =  cylinder

    (3.14)(4)2(5)

    (3.14)(16)(5)

    (50.24)(5)

    251.2=V of cy

    CONE:

    1/3 pi r2h

    1/3(3.14)(4)2(15)

    (1.47)(16)(15)

    (23.52)(15)

    352.8=V of cone

    NO MISTAKES!!!

    UNIQUE ANSWER!!

    (AND IT DESERVES BRAINLIEST!)

    SO PLS MARK BRAINLIEST

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