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 × 10 cm × 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.

• A. 550 $c{m}^3$
• B. 456.89 $c{m}^3$
• C. 576.63 $c{m}^3$
• D. 523.53 $c{m}^3$

Answer 1

The correct option is D

523.53 $c{m}^3$

Given,
Radius of each conical depression = r = 0.5 cm
Height of each conical depression = h' = 1.4 cm

Volume of wood in the entire stand = Volume of cuboid - volume of 4 identical conical depression

We know, volume of a cuboid is length × breadth × height and volume of a cone is $\frac{1}{3}\pi r^2{h}^{\prime }$.

Therefore, volume of wood in entire stand
$=(l\times b\times h)-(4\times \frac{1}{3}\pi r^2{h}^{\prime })$
$=(15\times 10\times 3.5)-(4\times \frac{1}{3}\times \frac{22}{7}\times 0.5\times 0.5\times 1.4)$

$=525-1.467$

$=523.53c{m}^3$