A solid is composed of a cylinder with hemispherical en
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solids 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.
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Right Answer is:
SOLUTION
Solution:
As per the parameters given in the question, we have
Radius of the hemispherical end (say r) = 7 cm
Height of the solid = (h + 2r) = 104 cm
The curved surface area of the cylinder (say S) = 2 πr h
S = 2 π ( 7 ) h …….E.1
⇒h+2r=104
⇒h=104−(2×7)
h = 90 cm
Put the value of h in E.1, we will get
S = 2 π (7) (90)
S = 3948.40 cm2
So, the curved surface area of the cylinder = S = 3948.40 cm2
Curved surface area of the two hemisphere (say SA) = 2 (2 πr2)
SA = 22π (7)2
SA = 615.75 cm2
Therefore, the total curved surface area of the solid = Curved surface area of the cylinder + Curved surface area of the two hemisphere = TSA
TSA = S + SA
TSA = 3948.40 + 615.75
TSA = 4571.8cm2 = 45.718 dm2
The cost of polishing the 1 dm2 surface of the solid is Rs. 15
So, the cost of polishing the 45.718 dm2 surface of the solid = 10 45.718 = Rs. 457.18
Hence,
The cost of polishing the whole surface of the solid is Rs. 457.18.