1.

A bucket is 32 cm in diameter at the top and 20 cm in diameter at the bottom. Find the capacity of bucket in litres if it is 21 cm deep. Also find the cost of tin sheet used in making the bucket at the rate of Rs 1.50 per sq dm.

Answer»

SOLUTION :Here R=16 cm , r=10 cm and h=21 cm
volume of frustum of a cone `=(pih)/(3)(R^(2)+r^(2)+Rr)`
`=(22)/(7)xx(1)/(3)xx21(16^(2)+10^(2)xx10)`
`=22xx516xx=11352 cm^(3)=(11352)/(1000)`litres=11.352 litres
Now for slant height l of furstum
`l^(2)=h^(2)+(R-r)^(2)`
`l^(2)=21^(2)+(16-10)^(2)`
`l^(2)=441+36`
`l^(2)=447`
`l=sqrt(447)`=21.84 cm
Now S.A of bucket =`pirl(R+r)+pir^(2)`
`=(22)/(7)xx21.84xx(16+10)+(22)/(7)xx10^(2)`
`=(22)/(7)(21.84xx26+100)`
`=(22)/(7)xx667.84=2098.9+2 cm^(2)=20.99 dm^(2)`
Cost of sheet @ 1.50 PER sq dm.
=`20.99xx1.50` =Rs 31.49


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