Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm3, then what is the slant height of the cone? (Use $\pi$ = 3.14)
Option 1: 12 cm
Option 2: 11 cm
Option 3: 13 cm
Option 4: 14 cm
Correct Answer: 13 cm
Solution : Given: The height and the radius of the base of a right circular cone = 12 : 5 Let the height be $12x$ and the radius is $5x$. Volume = 314 cm 3 We know that, Volume of a cone = $\frac{1}{3}\pi r^2 h$ ⇒ $314 = \frac{1}{3} × 3.14 × 5x × 5x × 12x$ ⇒ $100 = 100x^3$ ⇒ $x=1$ Radius $=5x=5\times1=5$ Height $=12x=12\times1=12$ Slant height = $\sqrt{\text{height$^2$ + radius$^2$}}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\ \text{cm}$ Hence, the correct answer is 13 cm.
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