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# 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 (see figure).

"

Given:

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.

To do:

We have to find the volume of the wood in the entire stand.

Solution:

Length of the cuboid pen stand $l = 15\ cm$

Breadth of the cuboid pen stand $b = 10\ cm$

Height of the cuboid pen stand $h = 3.5\ cm$

Therefore,

Volume of the cuboid pend stand $= lbh$

$= 15 \times 10 \times 3.5$

$= 525\ cm^3$

Radius of the conical depression $r = 0.5\ cm$

Height of the conical depression $h_1 = 1.4\ cm$

Volume of the conical depression $=\frac{1}{3} \pi r^2 h_1$

$=\frac{1}{3} \times \frac{22}{7} \times (0.5)^2 \times 1.4$

$=\frac{22 \times 0.5 \times 0.5\times0.2}{3}$

$=\frac{1.1}{3}$

$=0.366 \mathrm{~cm}^{3}$

The volume of four conical depressions $=4 \times$ Volume of the conical depression

$=4 \times 0.366$

$=1.47 \mathrm{~cm}^{3}$

The volume of wood in the entire pen stand $=$ Volume of the cuboidal pen stand $-$ Volume of 4 conical depressions

$=525-1.47$

$=523.53 \mathrm{~cm}^{3}$

The volume of the wood in the entire stand is \( 523.53 \mathrm{~cm}^{3} \).

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