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Mathematics

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

Mensuration

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Answer

Given,

Circumference of base = 66 m

⇒ 2πr = 66

2×227×r=662 \times \dfrac{22}{7} \times r = 66

⇒ r = 66×72×22=212\dfrac{66 \times 7}{2 \times 22} = \dfrac{21}{2} = 10.5 cm

By formula,

Volume of cone = 13πr2h\dfrac{1}{3}πr^2h

=13×227×(10.5)2×12=22×110.25×47=97027=1386 m3.= \dfrac{1}{3} \times \dfrac{22}{7} \times (10.5)^2 \times 12 \\[1em] = \dfrac{22 \times 110.25 \times 4}{7} \\[1em] = \dfrac{9702}{7} \\[1em] = 1386 \text{ m}^3.

Hence, volume of air contained in cone = 1386 m3.

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