The area of the base of a right circular cone is 1386 cm2 and its curved surface area is 1914 cm2. What is the volume of the cone? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9240 cm3
The base area \(\pi r^2\) gives the radius and the curved surface area \(\pi rl\) gives the slant height \(l\). The radius, the height and the slant height form a right triangle, so \(h=\sqrt{l^2-r^2}\). Then the volume is \(\frac{1}{3}\times\) base area \(\times h\).
\(\displaystyle\frac{22}{7}r^2=1386\), so \(r^2=441\) and \(r=21\) cm
\(\displaystyle\frac{22}{7}\times21\times l=1914\), so \(66l=1914\) and \(l=29\) cm
\(h=\sqrt{29^2-21^2}=\sqrt{841-441}=\sqrt{400}=20\) cm
Volume \(\displaystyle=\frac{1}{3}\times1386\times20=462\times20=9240\) cm3
