Q. 204.5( 12 Votes )

A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins, respectively. The dimensions of 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.

Answer :


For cuboidal stand,

Length, l = 10 cm

Breadth, b = 5 cm

Height, h = 4 cm

We know that

Volume of a cuboid = lbh

Where l, b and h are length, breadth and height respectively.


Volume of cuboidal stand = 10(5)(4) = 200 cm3

For one conical depression,

Radius, r = 0.5 cm

Height, i.e. depth, h = 2.1 cm

We know that

Where r is base radius and h is the height of the cone

For Cubical depression,

Side, a = 3 cm

We know that

Volume of cube = a3, where a is the side of the cube.

Volume of cubical depression = (3)3 = 27 cm3

Volume of wood in the entire stand = volume of cuboidal stand - volume of 4 conical depression - volume of one cubical depression.

Volume of wood = 200 - 4(5.5) - 27 = 170.8 cm3

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