Question

a hollow cylindrical pipe has inner circumference 44 dm and outer 45 dm. Find the cost of painting it from both sides (inside as well as outside) at ₹2 per meter sq if length is 3.5 m

Answer 1

Total area painted = inner C.S.A +outer C.S.A = 2πrh +2πRh =

inner C.S.A = 2πrh
outer C.S.A = 2πRh
inner circumference = 2πr = 44dm = 4.4 m
(∵ 1 m = 10 dm )
outer circumference = 2πR = 45 dm = 4.5 m

h = 3.5 m

Total area painted = 4.4 × 3.5 + 4.5 ×3.5
= 31.15 m²
Cost of painting 1 m² = Rs 2
Cost of painting 31.15 m² = 31.15 × 2
=Rs 62.3

Answer 2

Given data :

• A hollow cylindrical pipe has inner circumference 44 dm and outer 45 dm.
• The cost of painting it from both sides (inside as well as outside) at Rs 2 per m² and the length is 3.5 m.

To find : The cost of painting ?

Solution : HERE WE KNOW THAT FORMULA OF CIRCUMFERENCE IS : 2πr

According to given : Inner circumference of hollow cylindrical pipe = 2πr = 44 dm = 4.4 m _____( 1 )

and outer circumference of hollow cylindrical pipe = 2πr = 45 dm = 4.5 m. ______( 2 )

Let, length of hollow cylindrical pipe be height ( h ) of cylindrical pipe.

⟹ h = 3.5 m

Now by formula of curved surface area of cylinder :

⟹ inner C.S.A = 2πr * h

{from ( 1 )}

⟹ inner C.S.A = 4.4 * h

⟹ inner C.S.A = 4.4 * 3.5

⟹ inner C.S.A = 15.4 m²

Similarly,

⟹ outer C.S.A = 2πr * h

{from ( 2 )}

⟹ outer C.S.A = 4.5 * h

⟹ outer C.S.A = 4.5 * 3.5

⟹ outer C.S.A = 15.75 m²

Now,

⟹ cost of painting = 2 * ( inner C.S.A + outer C.S.A )

⟹ cost of painting = 2 * ( 15.4 + 15.75 )

⟹ cost of painting = 2 * 31.15

⟹ cost of painting = Rs 62.3

Answer : Hence cost of painting is Rs 62.3

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