Question

A pen stand is made of wood in the shape of cuboid with three concial depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer 1

Volume of cuboid $=$lbh

$=15\times 10\times 3.5=525c{m}^3$.

Volume of $3$ conical depressions $=3\times \frac{1}{3}\pi r^{2}h$

$=\pi \left(0.5{)}^2\right(1.4)=1.1c{m}^3$

Volume of wood $=525-1.1$

$=523.9c{m}^3$.