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Question
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm2 .
Solution
We have a solid composed of cylinder with hemispherical ends.
Radius of the two curved surfaces(r) = 7 cm
Height of cylinder is h.
Total height of the body(h + 2r) = 104 cm
So, total surface area is given by,
Total surface area = Curved surface area of cylinder +2(Curves surface area of hemisphere)
=`2pirh+2(2pir^2)`
= 2πr(h+2r)
=2(3.14)(7)(104) cm2
=4571.84 cm2
Change the units of curved surface area as,
Total surface area = `4571.87/100 dm^2`
= 45.7184 dm2
Cost of polishing the surface is Rs 10 per dm2.
So total cost,
= Rs(45.7184)(10)
= Rs 457.18
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