Question

The difference between the outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.​

Answer 1

$\huge\bold{Bonjour!!}$

$\huge\mathfrak\purple{Solution:-}$

⏩ Let the outer radius of the metallic cylindrical pipe be R and inner radius be r.

→ Outer surface Area - Inner Surface Area

= 44 cm²

That is,

2πRh - 2πrh = 44

=> 2π × 14(R-r) = 44

Therefore,

R-r = 44 × 7/ 2 × 22 × 14

= 1/2 cm .....→(i)

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Volume of metal = 99 cm³

πR²h - πr²h = 99

=> 14π (R² - r²) = 99

=> R² - r² = 99 × 7/ 22 × 14 = 9/4 cm²

=> (R + r) (R - r) = 9/4

=> R + r = 9/4 × 2 = 9/2 .....→ (ii)

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Now, on adding (i) and (ii), we get,

2R = 10/2

Therefore,

R = 5/2

=> R = 2.5 cm

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Now, from (ii),

r= 9/2 - 5/2

= 4/2 = 2 cm.

Therefore,

** Outer radius, R = 2.5 cm

and

** Inner radius, r= 2 cm.

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Answer 2

Step-by-step explanation:

Let the outer radius of the metallic cylindrical pipe be R and inner radius be r.

→ Outer surface Area - Inner Surface Area

= 44 cm²

That is,

2πRh - 2πrh = 44

=> 2π × 14(R-r) = 44

Therefore,

R-r = 44 × 7/ 2 × 22 × 14

= 1/2 cm .....→(i)

Volume of metal = 99 cm³

πR²h - πr²h = 99

=> 14π (R² - r²) = 99

=> R² - r² = 99 × 7/ 22 × 14 = 9/4 cm²

=> (R + r) (R - r) = 9/4

=> R + r = 9/4 × 2 = 9/2 .....→ (ii)

Now, on adding (i) and (ii), we get,

2R = 10/2

Therefore,

R = 5/2

=> R = 2.5 cm

Now, from (ii),

r= 9/2 - 5/2

= 4/2 = 2 cm.

Therefore,

** Outer radius, R = 2.5 cm

and

** Inner radius, r= 2 cm.