If the area of the base of a cone is 154 cm² and the area of its curved surface is 550 cm², then its volume is:

1232 cm³

We know that,

Volume of cone = \(\frac{1}{3}\)πr²h

Curved surface area of cone = πrl

Area of base of cone = πr²

We have,

Area of base of cone = 154 cm²

Area of curved surface = 550 cm²

\(\frac{22}{7}\) × r² = 154

= r² = (154 × 7) × \(\frac{1}{22}\)  

= r² = 49

= r = 7 cm

Curved surface area of cone = 550 = \(\frac{22}{7}\) × 7 × l

l =25

Now, h = \(\sqrt {l^2 – r^2}\)

= h = \(\sqrt {25^2 – 7^2}\) = \(\sqrt {625 – 49}\)

= h = 24

Volume of cone = \(\frac{1}{3}\) × \(\frac{22}{7}\) × 7 × 7 × 24

= 22 × 7 × 8 = 1232 cm³