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 dm^{2}.

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(2πr^{2})

= 2(2 ×π ×7^{2})

= 615.75 cm ……….. (3)

Total curved surface area = 2+3

= 3958.40 + 615.75

= 4574.15 cm^{2}

Cost of polishing for 1 dm^{2} = Rs.10

Cost of polishing for 54.75 dm^{2} = 45.74×10

= Rs.457.60

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PREVIOUSA vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.NEXTA cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic centimeters of cork dust will be required?

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