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    How much material is wasted when a solid cone of height 24 cm and radius 8 cm is recast into a solid cylinder of radius 6 cm and height 6 cm?
    Question

    How much material is wasted when a solid cone of height 24 cm and radius 8 cm is recast into a solid cylinder of radius 6 cm and height 6 cm?

    A.

    37.5%

    B.

    52%

    C.

    57.8%

    D.

    64%

    Correct option is C

    Given:

    Solid cone:
    Height = 24 cm
    Radius = 8 cm

    Solid cylinder:
    Height = 6 cm
    Radius = 6 cm

    Formula Used:

    Volume of a cone = (1/3)×π×r2×h (1/3) ×π × r^2 × h​​
    Volume of a cylinder = π×r2×h π × r^2 × h​​

    Solution:

    Volume of cone = (1/3)×π×82×24=(1/3)×π×64×24=512(1/3) × π × 8^2 × 24 = (1/3) × π × 64 × 24 = 512​π cubic cm

    Volume of cylinder = π×62×6=π×36×6=216ππ × 6^2 × 6 = π × 36 ×6 = 216π​ cubic cm

    Material wasted = Volume of cone - Volume of cylinder
    Material wasted = 512π - 216π = 296π cubic cm

    Required  percentage   = 296512×100\frac{296}{512}\times100

    = 57.8%

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