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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

4. 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 Fig. 13.16).

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The volume of wood is given by = volume of the cuboid - the volume of four cones.

Firstly, the volume of cuboid :    =\ lbh

or                                         =\ 15\times 10\times 3.5

or                                         =\ 525\ cm^3

And, the volume of cone :   

                                           \\=\ \frac{1}{3} \pi r^2h\\=\ \frac{1}{3} \pi \times (0.5)^2\times 1.4\\\\=\ 0.3665\ cm^3                      

Thus the volume of wood is   = 525 + 4 (0.3665) = 523.53 \:cm^3 

Posted by

Devendra Khairwa

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