A right circular cone has base radius 5 cm and height 12 cm. Consider the following statements:
I. The slant height of the cone is 17 cm.
II. The curved surface area of the cone is \(100\pi\) cm2.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither I nor II
The radius, the height and the slant height of a cone form a right triangle: \(l=\sqrt{r^2+h^2}\). The curved surface area \(=\pi rl\).
Statement I — Incorrect.
\(l=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13\) cm, not 17 cm (17 is just \(5+12\))
Statement II — Incorrect.
Curved surface area \(=\pi\times5\times13=65\pi\) cm2
\(100\pi\) is the volume in cm3: \(\frac{1}{3}\pi\times5^2\times12=100\pi\)
Neither statement is correct.
