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Question
A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 1/2` seconds at the rate of 9 complete rounds per second. Find the area covered by the cylinder in `4 1/2` seconds.
Solution
Circumference of cylinder = 8 cm
Therefore, radius = `c/(2pi) = (8 xx 7)/(2 xx 22) = 14/11 cm`
Length of the cylinder (h) = 21 cm
Curverd surface area = 2πrh
= `2 xx 22/7 xx 14/11 xx 21`
= 168 cm2
Area covered in one revolution = 168 cm2
Area covered in 9 revolution = 168 cm2 × 9 = 1512 cm2
Therefore, area covered in 1 second = 1512 cm2
Hence, area covered in `4 1/2` seconds = `1512 cm^2 xx 9/2`
= 6804 cm2
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