The area of the curved surface of the cone generated by the sector of a circle radius 6cm and arc length 22cm is (\(\pi\) = \(\frac{22}{7}\))

A.

58 sq.cm

B.

34 sq.cm

C.

132 sq.cm

D.

77 sq.cm

E.

66 sq.cm

Correct answer is E

Given: length of the arc AOB = 22cm ; L = 6cm

Curved surface area of cone = \(\pi\)rl

Length of an arc = \(\frac{\theta}{360}\) x 2 \(\pi\)L

= 22cm

but length of an arc = circumference of the cone = 2\(\pi\)

where r is the radius of the cone circle

2\(\pi\)r = 22, r = \(\frac{22}{2\pi}\)r

= 11 x \(\frac{7}{22}\)

= \(\frac{7}{2}\)

curved surface area = \(\pi\)rl

= \(\frac{22}{7}\) x \(\frac{7}{2}\) x 6

= 66 sq.cm