If the diameter of the base of a cone is 18 cm and its curved surface area is $424\frac{2}{7} cm^2$, then its height will be: (Take $ \pi = \frac{22}{7}$)

12 cm

Given that,

Curved surface area is $424\frac{2}{7} cm^2$ = \(\frac{2970}{7}\)

The diameter of the cone = 18

Then, Radius of cone = \(\frac{18}{2}\) = 9 cm

We know that,

Curved surface area of cone = πrl

= πrl = \(\frac{2970}{7}\)

= (22/7 × 9 × l) = \(\frac{2970}{7}\)

= (\(\frac{198}{7}\)) l = \(\frac{2970}{7}\)

= l = 2970 × \(\frac{7}{198}\)× 7) 

= l = 15 cm

Now, we also know that,

l² = r² + h²

= (15)² = (9)² + h²

= 225 = 81 + h²

= h² = (225 – 81)

= h² = 144

= h = 12 cm