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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 by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of the wood in the entire stand, correct to 2 decimal places.

Answer:

**Solution:**

Here to get the volume of wood need to make the stand, we neeed to subtract volume of cuboid and volume of four conical depressions.

Dimensions of the cuboid = 15 cm× 10 cm × 3.5 cm

Volume of the cuboid = 15×10×3.5 = 525 cm^{3}

Radius of each depression, r = 0.5 cm

Depth, h = 1.4 cm

Volume of conical depression = (1/3)π r^{2}h

= (1/3)×(22/7)×0.5^{2}×1.4

= 22×0.25×1.4/21

= 7.7/21 cm^{3}

Volume of 4 such conical depressions = 4×7.7/21

= 1.467 cm^{3}

Volume of wood in the stand = Volume of the cuboid- Volume of 4 conical depressions

= 525-1.467

= 523.533

= 523.53 cm^{3}

**Hence the volume of the wood in the stand is 523.53 cm ^{3}.**

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