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Question
The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm2 is
Options
Rs. 1582.50
Rs. 1724.50
Rs. 1683
Rs. 1642
Solution
Radius of top of bucket `r_1 = 42 / 2 = 21 "cm"`
Radius of bottom of bucket `r_2 = 28 / 2 = 14 "cm"`
Height of bucket, h = 24 cm.
`l = sqrt(h^2 (r_1 - r_2))`
`=sqrt(576 + (21 - 14)^2)`
`= sqrt (576 + 49)`
`=sqrt 625`
`= 25`
C.S.A. of the bucket
`= pi (r_1 + r_2)l`
`=pi (21 +14) xx 25`
`=22/7 xx 35 xx 25`
= 2750 cm2
Area of bottom
`=pir^2`
`= 22 /7 xx 196`
`= 616 \ cm^2`
The cost of painting its C.S. ,
`=(2750 + 616) xx 1/2`
`=3366 xx 1/2`
`="Rs" 1683`
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