Question

3. The circumference of the base of a 12 m high
conical tent is 66 m. Find the volume of the
air contained in it.
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Answer 1

Given:

The circumference of the conical tent is 66m

The height of the conical tent is 12 m

To be found:

The volume of the air contained in it.

(so we have to find the volume of the conical tent.)

$\underline{\sf{The\ formula\ for\ finding\ the\ volume\ of\ cone}}$

$\boxed{\red{\rm{\frac{1}{3}\pi r^{2}h}\ \bf unit\ sq.}}$

So,

We have h = 12m

We need radius = r =?

As given that the circumference of the conical tent is 66m

So,

$\implies 2\pi r = 66$

$\implies 2\times \frac{22}{7} \times r = 66$

$\implies \frac{44}{7} \times r = 66$

$\implies r = 66 \times \frac{7}{44}$

$\implies r = \frac{6 \times 7}{4}$

[66/11 = 6 and 44/11 = 4]

$\implies r = \frac{3\times 7}{2}$

$\therefore r = \boxed{\frac{21}{2}m}\ or\ \boxed{\bf 10.5m}$

Now,

Finding the Volume,

$= \frac{1}{3} \pi r^{2}h$ unit sq.

$= \frac{1}{3} \times \frac{22}{7} \times (\frac{21}{2})^{2} \times 12$

$= \frac{1}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times 12$

$= \boxed{9702m^{2}}$

Hence,

The volume of the air contained in it is 9702 m sq.

Answer 2

Given ,

The circumference of the base of a 12 m high conical tent is 66 m

As we know that ,

The circumference of circle is given by

$\boxed{ \tt{Circumference = 2\pi r}}$

Thus ,

66 = 2 × 22/7 × r

66 = 44/7 × r

6/4 = 1/7 × r

r = (3 × 7)/2

r = 21/2 m

Now , the volume of cone is given by

$\boxed { \tt{Volume = \frac{1}{3} \pi {(r)}^{2} h} }$

Thus ,

V = 1/3 × 22/7 × 21/2 × 21/2 × 12

V = 9702 sq. m