Q. 14

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.

Answer :

Radius of hemispherical ends, r = 7 cm


Height of body (h + 2r) = 104 cm


Curved surface area of cylinder = 2πrh


= 2π (7)h ……….(1)


Given: h + (2r) = 104 cm


h = 104 – 2 (7)


h =90 cm


Substitute the value of h in eq. (1),


Curved surface area of cylinder = 2π (7) (90)


= 3958.40 cm …..(2)


Curved area of 2 hemisphere = 2(2πr2)


= 2(2 ×π ×72)


= 615.75 cm ……….. (3)


Total curved surface area = 2+3


= 3958.40 + 615.75


= 4574.15 cm2


Cost of polishing for 1 dm2 = Rs.10


Cost of polishing for 54.75 dm2 = 45.74×10


= Rs.457.60


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