JAMB - Mathematics (1982 - No. 33)
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
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 = \(\frac{22}{2\pi}\)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
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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