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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 is 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. What is the volume of the wood in the entire stand?

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177 cm³

180 cm³

170.8 c m 3

190 cm³

answer is C.

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Detailed Solution

Given that, the dimension of the cuboid is 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.
The volume of the cones is given by:

V = 13 π r 2 h V = 13 × 227 × 0.5 2 × 2.1 V = 0.55 c m 3

There are 4 such cones depressed in the wooden cuboid. So, the volume of the cones is

4 × 0.55

, that is,

V 1 = 2.2 c m 3

The volume of the cube,

V 2 = a 3 V 2 = 33 V 2 = 27 c m 3

The volume of the wooden cuboid,

V 3 = l × b × H V 3 = 10 × 5 × 4 V 3 = 200 c m 3

The volume of the wood in the entire stand,

V = V 3 − V 1 − V 2 V = 200 − 2.2 − 27 V = 170.8 c m 3

The volume of the wood in the entire stand is

170.8 c m 3

.
Therefore, the correct option is 3.

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