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

1. 15 m

2. 12 m

3. 9 m

4. 24 m

Given, Area of base = 154 m²

⇒ πr² = 154

$\Rightarrow \dfrac{22}{7} \text{r}^2 = 154 \\[1em] \Rightarrow \text{r}^2 = 154 \times \dfrac{7}{22} \\[1em] \Rightarrow \text{r}^2 = \dfrac{1078}{22} \\[1em] \Rightarrow \text{r}^2 = 49 \\[1em] \Rightarrow \text{r} = \sqrt{49} \\[1em] \Rightarrow \text{r} = 7 \text{ m.}$

Volume of cone = 462 m³

By formula,

Volume of cone = $\dfrac{1}{3}$ πr²h

$\Rightarrow 462 = \dfrac{1}{3} \times \dfrac{22}{7} \times 7^2 \times \text{h} \\[1em] \Rightarrow 462 = \dfrac{22}{21} \times 49 \times \text{h} \\[1em] \Rightarrow \text{h} = \dfrac{462 \times 21}{22 \times 49} \\[1em] \Rightarrow \text{h} = \dfrac{9702}{1078} \\[1em] \Rightarrow \text{h} = 9 \text{ m}.$

Hence, option 3 is the correct option.