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Mathematics

The volume of a conical tent is 462 m3 and the area of the base 154 m2. The height of the conical tent is :

  1. 15m

  2. 12 m

  3. 9 m

  4. 24 m

Mensuration

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Answer

Given, volume of a conical tent = 462 m3 and the area of the base = 154 m2

Using formula,

area of base = πr2 and volume of cone = 12\dfrac{1}{2} πr2h

⇒13πr2h=462⇒13×(πr2)×h=462⇒13×154×h=462⇒1543×h=462⇒h=3×462154⇒h=1386154⇒h=9 m.\Rightarrow \dfrac{1}{3}πr^2h = 462 \\[1em] \Rightarrow \dfrac{1}{3} \times (πr^2) \times h = 462 \\[1em] \Rightarrow \dfrac{1}{3} \times 154 \times h = 462 \\[1em] \Rightarrow \dfrac{154}{3} \times h = 462 \\[1em] \Rightarrow h = \dfrac{3 \times 462}{154} \\[1em] \Rightarrow h = \dfrac{1386}{154} \\[1em] \Rightarrow h = 9 \text{ m}.

Hence, option 3 is the correct option.

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