A sector as shown in the figure is assembled to form a cone. What is the base radius (in cm) of the cone so formed? \(\left(\pi=\frac{22}{7}\right)\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5.25
When a sector is folded into a cone, its radius becomes the slant height and its arc becomes the circumference of the base. So the arc length of the 210° sector equals \(2\pi r\), where \(r\) is the base radius.
Arc length of the sector (210° out of the full circle of radius 9 cm) \(\displaystyle=\frac{210}{360}\times2\pi\times9\)
This arc becomes the base circumference: \(\displaystyle 2\pi r=\frac{210}{360}\times2\pi\times9\)
Base radius \(\displaystyle r=\frac{210}{360}\times9=\frac{7}{12}\times9=5.25\) cm
The value of \(\pi\) cancels, so \(\frac{22}{7}\) is not needed.