A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm² .[Use π = 3.1416]
Answers
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:
radius of the cylinder =r
1
=18cm
height of the cylinder h=72cm
total surface area
= curved surface are of the cylinder + surface areas of hemispherical ends
=(2πrh+2×2πr
2
)cm
2
=(2πrh+4πr
2
)cm
2
=2πr(h+2r)cm
2
=2×
7
22
×18×(72+36)cm
2
=12219.42cm
2
Rate of polishing 7 paise per sq.cm
Cost of polishing =Rs.(12219.42×
100
7
)
=Rs.855.36Rs