Question

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 dimension of the cuboid are  \[10 cm \times 5 cm \times 4 cm\].

The radius of each of the conical depression 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 1

The dimensions of the cuboid = 10 cm × 5 cm × 4 cm
Volume of the total cuboid = 10 cm × 5 cm × 4 cm = 200 cm³ 
Radius of the conical depressions, r = 0.5 cm
Depth, h = 2.1 cm
Volume of the conical depression = 

\[\frac{1}{3} \pi r^2 h = \frac{1}{3}\pi \left( 0 . 5 \right)^2 \left( 2 . 1 \right) = 0 . 5495\]cm³
Edge of cubical depression, a = 3 cm
Volume of the cubical depression =  \[a^3 = 3^3 = 27 c m^3\]

Volume of wood used to make the entire stand = Volume of the total cuboid − volume of conical depression − volume of cubical depression 

\[= 200 - 4 \times 0 . 5495 - 27\]

\[ = 170 . 802 c m^3 \]