Question

A solid is composed of a cylinder with hemispherical ends if whole length of the solid is 108 cm and the diameter of the hemispherical ends is 36 cm find the cost of polishing its surface at the rate of 70 paise per square cm

Answer 1

Answer:

The cost of polishing the surface of the solid is ₹ 855.02

Step-by-step explanation:

SOLUTION :  

Given :  

Let h be the height of a cylinder

Diameter of the cylinder = 36 cm

Radius of the cylinder = Radius of the hemispherical end , r = 36/2 = 18 cm

Height of the whole solid = 108 cm

Diameter of the hemisphere = height of the hemisphere =  2r  

Height of a cylinder + height of a hemisphere = height of a solid  

h + 2r = 108 ………………..(1)

h = 104 - 2r = 104 - 2 × 18 = 108 - 36 = 72  

h = 72 cm

Height of a cylinder ,h = 72 cm

Total curved surface area of the solid = Curved surface area of the cylinder + Curved surface area of the two hemisphere  

= 2πrh + 2(2πr²)

= 2πrh + 4πr² = 2πr(h + 2r)

= 2πr(h + 2r)

= 2 × 3.1416 × 18(108)  

[From eq 1]

Total curved surface area of the solid = 12,214.54 cm²

Given : cost of polishing the 1 cm² @ rate of 7 paise

cost of polishing the 12,214.54 cm² surface of the solid = 7/100 × 12,214.54 =  0.07  × 12,214.54  =  ₹ 855.02

Hence, the cost of polishing the surface of the solid is ₹ 855.02 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

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Hello...

Q :- A solid is composed of a cylinder with hemispherical ends if whole length of the solid is 108 cm and the diameter of the hemispherical ends is 36 cm find the cost of polishing its surface at the rate of 70 paise per square cm.

A :- Radius of hemisphere=36/2=18

In the given solid height of cylinder = 108 - 2{radius of hemisphere}

= 108 - 18 = 90

CSA of the solid = CSA of cylinder + CSA of both hemispheres

= 2*22/7*18*90 + 2 (2*22/7*18*18) = 14256 cm^2

Cost = 14256 *70 = Rs 9980

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