Question

1. A hollow cylindrical pipe has inner circumference 44dm and outer circumference 45dm. Find the cost of painting it from both sides (inside and outside) at Rs.2 per m 2 if its length is 3.5m.

Answer 1

10dm = 1m

Inner
2 x 22/7 x r = 4.4      ⇒ r = 0.7 m
Inner surface area = 2 x 22/7 x 0.7 x 3.5 = 15.4 cm²

Outer
2 x 22/7 x R = 4.5      ⇒ R = 0.716 m

Inner surface area = 2 x 22/7 x 0.716 x 3.5 = 15.752

Total surface area = 15.4 + 15.752 = 31.152 m²

Cost of painting = 2 x 31.152 = Rs. 62.30

Answer 2

Solution:-

Inner circumference = 44 dm or 44/10 = 4.4 m
Circumference = 2πr 
4.4 = 2*22/7*r
r = 30.8/44
Inner radius = 0.7 m
Outer circumference = 45 dm or 45/10 = 4.5 m
4.5 = 2*22/7*r
r = 4.5*7/44
r = 31.5/44
Outer radius = 0.716 m
Inner curved surface area = 2πrh
= 2*22/7*0.7*3.5
Inner curved surface area = 15.4 sq m
Outer curved surface area = 2*22/7*0.716*3.5
Outer surface curved area = 15.75 sq m
Total curved surface area =  15.4 + 15.75
= 31.15 sq m
Cost of painting it from both sides (inside and outside) = Rs. 2 per sq m
Total cost of painting = 31.15*2
= Rs. 62.30
Answer.