A right angle sector of radius r cm is rolled up into a cone by joining along the radius. Then the curved surface area of the cone is?

\(\frac{\pi}{4} r^2\)

R = radius of the base of cone

r = radius of circle

Circumference of base of cone= \(2 \pi R = \frac{2 \pi r}{4}\)

Therefore, radius of base (R) = \(\frac{r}{4}\)

slant height = r

C.S.A. = \(\pi \)Rl = \(\pi \)(\(\frac{r}{4}\))r

                           =  \(\frac{\pi}{4} r^2\)