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Question

# Question 20 A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

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Solution

## Given that, length of cuboid pen stand (l) = 10 cm Breadth of cuboid pen stand (b) = 5 cm And height of cuboid pen stand (h) = 4 cm ∴ Volume of cuboid =l×b×h=10×5×4 = 200 cm3 Also, radius of conical depression (r) = 0.5 cm And height of (depth) of a conical depression h1=2.1 cm ∴ Volume of a conical depression = 13πr2h1 =13×227×0.5×0.5×2.1=22×5×51000=2240=1120=0.55 cm3 Also , given Edge of cubical depression (a)= 3cm volume of cubical depression = (a)3=(a)3=27 cm3 So, volume of 4 conical depression =4×1120=115 cm3 Hence the volume of wood in the entire pen stand = Volume of cuboid pen stand – Volume of 4 conical Depressions – Volume of a cuboid depressions =200−115−27=200−1465=200 − 29.2 = 170.8 cm3 So, the required volume of the wood in the entire stand is 170.8 cm3.

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