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Mathematics · Surface Areas and Volumes · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 12 · NCERT Examples

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NCERT Example

Example 5

industrial shed · combined volume

A shed is a cuboid surmounted by a half-cylinder. Its base is 7 m × 15 m and its cuboidal part is 8 m high. Find the volume of air it can hold. Machinery occupies 300 m³ and 20 workers occupy 0.08 m³ each. Find the air left in the occupied shed. Take π = 22/7.

Industrial shed formed by a cuboid and half-cylinder roof, labelled 15 metres, 7 metres and 8 metres.
Figure 12-12 from the supplied NCERT chapter.

Solution

Board-exam working:

Cuboid dimensions: 15 m × 7 m × 8 m.

Vc=15×7×8=840 m3V_c=15\times7\times8=840\text{ m}^3

The half-cylinder has radius 7/2 m and length 15 m.

Vh=12πr2lV_h=\frac12\pi r^2l
=12×227×(72)2×15=288.75 m3=\frac12\times\frac{22}{7}\times\left(\frac72\right)^2\times15=288.75\text{ m}^3

Total empty volume:

V=840+288.75=1128.75 m3V=840+288.75=1128.75\text{ m}^3

Space occupied by workers:

20×0.08=1.6 m320\times0.08=1.6\text{ m}^3

Air left after machinery and workers occupy space:

1128.75−(300+1.6)=827.15 m31128.75-(300+1.6)=827.15\text{ m}^3

Final answer

Vempty=1128.75 m3,Vair=827.15 m3V_{empty}=1128.75\text{ m}^3,\qquad V_{air}=827.15\text{ m}^3