Practicing Success
The area of the base of a cone is 314 cm² and the curved surface area is 628 cm². The volume of this cone will be (take \(\pi \) = 3.14)? |
\(\frac{314\sqrt {2}}{3}\) cm³ \(\frac{3140\sqrt {2}}{3}\) cm³ \(\frac{314\sqrt {3}}{3}\) cm³ \(\frac{3140\sqrt {3}}{3}\) cm³ |
\(\frac{3140\sqrt {3}}{3}\) cm³ |
Area of base = \(\pi \)r2 ⇒ 314 = \(\pi \)r2 ⇒ r = 10 cm (Take \(\pi \) = 3.14) C.S.A. = \(\pi \)rl ⇒ 628 = 3.14 × 10 × l ⇒ l = 20 cm h = \(\sqrt {l^2 - r^2}\) = \(\sqrt {400 - 100}\) = \(\sqrt {300}\) = 10\(\sqrt{3}\) Volume = \(\frac{1}{3}\) \(\pi \)r2h = \(\frac{1}{3}\) × 3.14 × 100 × 10\(\sqrt{3}\) = \(\frac{3140\sqrt {3}}{3}\) cm3 |