Find the curved surface area of a cone having base diameter 42 cm and height 20 cm. \(\left(\pi=\frac{22}{7}\right)\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(1914\,\mathrm{cm^2}\)
The curved surface area of a cone is \(\pi rl\), where \(l\) is the slant height. The radius, height and slant height form a right triangle, so \(l=\sqrt{r^2+h^2}\).
Radius \(r=42\div2=21\) cm, height \(h=20\) cm
\(l=\sqrt{21^2+20^2}=\sqrt{441+400}=\sqrt{841}=29\) cm
CSA \(\displaystyle =\frac{22}{7}\times21\times29=66\times29=1914\,\mathrm{cm^2}\)