A right angled sector of radius r cm is rolled up into a cone in such a way that the two binding radii are joined together. Then the curved surface area of the cone is

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \Rightarrow \text{Circumference of sectors}=\frac{\pi r}{2}\\ & \Rightarrow \text{Circumference of base of cone of radius}=2\pi r_1\\ & \frac{\pi r}{2}=2\pi r_1\Rightarrow r_1=\frac{r}{4}\\ & \therefore \text{Radius of cone}=\frac{r}{4}\\ & \text{Curved surface area of cone}=\pi r_{1}l\\ & l=\text{slant height}\\ & l=r\\ & \therefore \text{Surface area of cone}=\pi \times \frac{r}{4}\times r\Rightarrow \frac{\pi r^2}{4}\end{array}$$