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.
Answers
Answer:
The cost of polishing the surface of the solid is ₹ 457.60.
Step-by-step explanation:
SOLUTION :
Given :
Let h be the height of a cylinder
Radius of the hemispherical end , r = 7 cm
Height of the solid = 104 cm
Diameter of the hemisphere = height of the hemisphere = 2r
Height of a cylinder + height of a hemisphere = height of a solid
h + 2r = 104 ………………..(1)
h = 104 - 2r = 104 - 2×7 = 104 - 14 = 90
h = 90 cm
Height of a cylinder ,h = 90 cm
Total curved surface area of the solid = Curved surface area of the cylinder + Curved surface area of the two hemisphere
TSA = 2πrh + 2(2πr²)
TSA = 2πrh + 4πr² = 2πr(h + 2r)
TSA = 2πr(h + 2r)
= 2 × 22/7 × 7(104)
[From eq 1]
TSA = 44 × 104 = 4576 cm² = 4576/100 dm²
[1cm² = 1/100 dm²]
TSA = 45.76 dm²
Given : cost of polishing the 1 dm² @ rate of ₹15
cost of polishing the 45.76 dm² surface of the solid = 10 × 45.76 = ₹ 457.60
Hence, the cost of polishing the surface of the solid is ₹ 457.60.
HOPE THIS ANSWER WILL HELP YOU….
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