The area of the curved surface of the cone generated by the sector of a circle radius 6cm and are length 22cm is ((pi) = (frac{22}{7}))
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A.
58 sq.cm -
B.
34 sq.cm -
C.
132 sq.cm -
D.
77 sq.cm -
E.
66 sq.cm
Correct Answer: Option E
Explanation
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}{2pi})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