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.
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