The curved surface area of a cone is 550 $$cm^2$$. If the area of its base is 154 $$cm^2$$, then what will be the volume of the cone?

Area of base of a cone $$=\pi r^2$$
Given, $$\pi r^2 = 154$$
=> $$\dfrac{22}{7} r^2 = 154$$
=> $$r^2 = 49$$
=> r = 7
Radius of the base of the cone = 7 cm
Given, Curved Surface Area of the cone $$= 550 cm^2$$
$$\dfrac{22}{7}\times7\times L = 550$$ where L = Slant height of the cone
=> L = 25 cm
Volume of the cone = $$\dfrac{1}{3}\pi r^2 (\sqrt{L^2 - r^2}) = \dfrac{1}{3}\times\dfrac{22}{7}\times \sqrt{25^2 - 7^2} = \dfrac{1}{3} \times \dfrac{22}{7} \times 576 = 1231.5 cm^2 \approx 1232 cm^2$$