Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

A

523.53 cm3

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B

550 cm3

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C

576.63 cm3

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D

456.89 cm3

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Solution

The correct option is A 523.53 cm3 Given, Radius of each conical depression = r = 0.5 cm Height of each conical depression = h' = 1.4 cm Volume of wood in the entire stand = Volume of cuboid - volume of 4 identical conical depression We know, volume of a cuboid is length × breadth × height and volume of a cone is 13πr2h′. Therefore, volume of wood in entire stand =(l×b×h)−(4×13πr2h′) =(15×10×3.5)−(4×13×227×0.5×0.5×1.4) =525−1.467 =523.53 cm3

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