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

58 sq.cm

34 sq.cm

132 sq.cm

77 sq.cm

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

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