the difference between outside and inside surface of a cylindrical metal pipe 14 cm long is 44 CM square if the pipe is made of outer and inner radii of the pipe
Answers
Let r and R be the inner and outer radius of the cylindrical metallic pipe respectively.
h be the height of the metallic pipe = 14 cm
Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder = 2πRh - 2πrh.
Given that difference between the outside and inside curved surface area of cylinder is 44 cm2 .
⇒ 2πh( R - r) = 44
⇒ 44 / 7 x 14 ( R - r) = 44
⇒ R - r = 1 / 2 = 0.5 ----------(1)
Given the pipe is made up of 99 cubic cm of metal so that
Volume of cylindrical metallic pipe = πR2h - πr2h.
⇒ 22/7 x 14 (R2 - r2) = 99 cm3 .
⇒ 44 x (R2 - r2) = 99
⇒ (R2 - r2) = 9 / 4 = 2.25
⇒ ( R - r)(R + r) = 2.25
= (0.5)x(R + r) = 2.25
R + r = 2.25 / 0.5 = 4.5
R + r = 4.5 ------------ (2)
Adding (1) and (2) we get
2R = 4.5 + 0.5 = 5
∴ R = 2.5 cm and r = 2 cm
∴ Outer side radius R = 2.5 cm and inner side radius r = 2 cm.
Hope this helps :)
Answer:
2.5,2
Step-by-step explanation: