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}$)
Answer & explanation
Correct answer: option 2
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