The area of the base of a cone is 616 cm² and the curved surface area is 2200 cm². The volume of this cone will be:
Answer & explanation
Correct answer: option 3
Area of base = \(\pi \)r² = 616
⇒ r2 = \(\frac{616\;×\;7}{22}\) = 196
⇒ r = 14
CSA = \(\pi \)rl = 2200
⇒ l = \(\frac{2200\;×\;7}{22\;×\;14}\) = 50
⇒ l = 50
Using Pythagoras theorem.
h = \(\sqrt {l^2 - r^2}\) = \(\sqrt {50^2 - 14^2}\) = 48
Now, Volume = \(\frac{1}{3}\) × \(\pi \)r²h = \(\frac{1}{3}\) × \(\frac{22}{7}\) × 196 × 48 = 9856 cm³