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Question

A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm × 3 cm × 4 cm. Find the volume of wood in the solid object.

A
3918 cm3
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B
7024 cm3
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C
1444 cm3
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D
789 cm3
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Solution

The correct option is C 1444 cm3
Given:
Height of the cylinder = 10 cm
Radius of the cylinder = 7 cm
Dimensions of the cuboid = 2 cm×3 cm×4 cm

Volume of cylinder=Vc
Volume of cuboidal depressions=Vd


Volume of the object =Vc4×Vd

Volume of cylinder, Vc = πr2h
Vc=227×72×10
Vc=1540 cm3

Volume of 4 cuboidal depressions
=4Vd
=4×l×b×h
=4×2×3×4
=96 cm3

Now, volume of the solid object
=154096=1444 cm3

Volume of wood in the solid object =1444 cm3

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