Surface Areas and Volumes — Question 3

Given,

Radius of the conical vessel (r) = 7 cm

Slant height of the conical vessel (l) = 25 cm

Let height of cone = h cm

We know that,

⇒ l² = r² + h²

⇒ h² = l² - r²

⇒ h = $\sqrt{l^2 - r^2}$

Substituting values we get :

$\Rightarrow h = \sqrt{(25)^2 - (7)^2} \\[1em] \Rightarrow h = \sqrt{625 - 49} \\[1em] \Rightarrow h = \sqrt{576} = 24 \text{ cm}.$

By formula,

Capacity of the conical vessel (V) = $\dfrac{1}{3}πr^2h$

Substituting values we get :

$V = \dfrac{1}{3} \times \dfrac{22}{7} \times 7^2 \times 24 \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times 49 \times 24 \\[1em] = 22 \times 7 \times 8 \\[1em] = 1232 \text{ cm}^3.\\[1em] = 1232 \times \Big(\dfrac{1}{1000}\Big) \text{ l} \quad [∵ 1000 \text{ cm}^3 = 1 \text{ litre] }\\[1em] = \text{1.232} \text{ l}.$

Hence, capacity of the conical vessel = 1.232 l.