The area of the base of a cone is 616 cm2 and its curved surface area is 2200 cm2. What is the volume of the cone? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9856 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 \(\displaystyle \frac{1}{3}\times\) base area \(\times h\).
\(\displaystyle \frac{22}{7}r^2=616\), so \(r^2=196\) and \(r=14\) cm
\(\displaystyle \frac{22}{7}\times14\times l=2200\), so \(44l=2200\) and \(l=50\) cm
\(h=\sqrt{50^2-14^2}=\sqrt{2500-196}=\sqrt{2304}=48\) cm
Volume \(\displaystyle =\frac{1}{3}\times616\times48=616\times16=9856\) cm3
