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.
Given,
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.
So,
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