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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