Question

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

Answer 1

Depth (h) of each conical depression $=1.4$ cm
Radius (r) of each conical depression $=0.5$ cm

$\text{Volume of wood = Volume of cuboid - 4 (Volume of a conical depression)}$
$=l\times b\times h-4\times \frac{1}{3}\pi r^{2}h$

$=15\times 10\times 3.5-4\times \frac{1}{3}\times \frac{22}{7}\times {\left(\frac{1}{2}\right)}^2\times 1.4$

$=525-1.47$

$=523.53{\text{cm}}^3$