Question

The difference between the outside and inside surfaces of a cylindrical metallic pipe 14cm long is 44cm^2. If the pipe is made of 99 cu. cm of metals then find the inner and outer radii of the pipe.

Guys add solution as well please

Answer 1

Answer:

r=2 R=2.5

Step-by-step explanation:

Solution:-

Let the outer radius be 'R' and the inner radius be 'r'

Given : Height = `14 cm

Outer Surface Area  - Inner Surface Area = 44 sq cm

⇒ 2πRh - 2πrh = 44

⇒ 2*22/7(R - r) × 14 = 44

⇒ (R - r) = (44 × 7)/(44 × 14)

(R - r) = 1/2 cm  ..........(1)

Now, 

Volume of the metallic pipe = 99 cu cm

πr²h = 99 cu cm

22/7 × (R² - r²) × 14 = 99

22/7 × (R + r) × (R - r) × 14 = 99

Putting the value of (R - r) = 1/2 in the above, we get.

22/7 × (R + r) × 1/2 × 14 = 99

(R + r) = (99 × 2 × 7)/(22 × 14)

(R + r) = 99/22 = 9/2 cm ..............(2)

Adding (1) and (2), we get.

R - r + R + r = 1/2 + 9/2

R + R = 10/2

2R = 5

R = 5/2 

R = 2.5 cm

Now, 

From (2), we get.

2.5 + r = 9/2 

r = 9/2 - 2.5

r = 4/2

r = 2 cm

Hence, the outer radius is 2.5 cm and inner radius is 2 cm