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Volumes Practice Test 1

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Question : 7 of 40

Marks: +1, -0

The vertical height of a conical tent is

4\frac{2}{3}

m and the diameter of its base is 6 m. It can be accommodate 11 persons. Find the average air space allowed per head.

2 $\mathrm{m}^3$
3 $\mathrm{m}^3$
4 $\mathrm{m}^3$
5 $\mathrm{m}^3$

Solution: 👈: Video Solution

Concept:

The average air space per person is the cone’s volume divided by the number of persons.

Explanation:

Height

h = 4\frac{2}{3} = \frac{14}{3}\,\mathrm{m}

.

Diameter

= 6\,\mathrm{m}

, so radius

r = 3\,\mathrm{m}

.

Volume of cone

= \frac{1}{3}\pi r^2 h

.

Substitute values:

V = \frac{1}{3} \times \frac{22}{7} \times (3)^2 \times \frac{14}{3}

.

Simplify:

V = 44\,\mathrm{m}^3

.

Average air space allowed per head

= \frac{V}{11} = \frac{44}{11}

.

So, average air space

= 4\,\mathrm{m}^3

.

Answer:

4\,\mathrm{m}^3

(Option C).

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