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.

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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