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    A cone of height 8 cm and base radius 4 cm is carved from a rectangular block of wood 8 cm × 6 cm × 4 cm. The percentage of wood wasted is approximate
    Question

    A cone of height 8 cm and base radius 4 cm is carved from a rectangular block of wood 8 cm × 6 cm × 4 cm. The percentage of wood wasted is approximately:

    A.

    56%

    B.

    30%

    C.

    58%

    D.

    48%

    Correct option is B

    Given:
    Cone: height (h) = 8 cm, radius (r) = 4 cm
    Rectangular block: length = 8 cm, breadth = 6 cm, height = 4 cm
    Formula Used:
    Volume of a cone = 13πr2\frac13πr^2​h,
    Volume of a rectangular block = length × breadth × height.
    Percentage waste=(Volume of blockVolume of coneVolume of block)×100%\text{Percentage waste} = \left( \frac{\text{Volume of block} - \text{Volume of cone}}{\text{Volume of block}} \right) \times 100\%​​
    Solution:
    => Volume of cone = 13π(4)2\frac 13π(4)^2​ × (8) = 134.041 cubic cm
    => Volume of block = 8 × 6 × 4 = 192 cubic cm
    => Waste = 192 - 134.041 = 57.959 cubic cm
    => Percentage waste = 57.959192\frac{57.959}{192}​ × 100% ≈ 30%

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