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? $\left(π=\frac{22}{7}\right)$

5.25

Note:

When a cone is formed from a sector of circle, then the following facts is to noticed:

1. Radius of the sector becomes Slant Height of the cone.

2. Length of Arc of the sector becomes circumference of the base of the cone.

3. Area of the sector becomes Curved Surface Area of the cone.

Now, according to the question:

Let r = radius of the sector and R = radius of the base of the cone.

From the above point no. 2:

⇒ Length of Arc of the sector = circumference of the base of the cone

⇒ 2πr × \(\frac{θ}{360°}\) = 2πR

⇒ 9 × \(\frac{210°}{360°}\) = R

⇒ \(\frac{21}{4}\) = R

⇒ R =5.25