The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 sq cm. If the pipe is made of 99 cu cm of metal, find the outer and inner radii of the pipe.
Answers
The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 sq cm. If the pipe is made of 99 cu cm of metal, find the outer and inner radii of the pipe. This answer is picture
Answer:
Solution: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⇒44/7×14 ( R - r) = 44
7×14 ( R - r) = 44⇒ R - r = 1/2= 0.5 ----------(1)
= 0.5 ----------(1)Given the pipe is made up of 99 cubic cm of metal so that
= 0.5 ----------(1)Given the pipe is made up of 99 cubic cm of metal so thatVolume of cylindrical metallic pipe = πR2h - πr2h.
= 0.5 ----------(1)Given the pipe is made up of 99 cubic cm of metal so thatVolume of cylindrical metallic pipe = πR2h - πr2h.⇒22/7x14 (R2 - r2) = 99 cm3 .
14 (R2 - r2) = 99 cm3 .⇒ 44× (R2 - r2) = 99
14 (R2 - r2) = 99 cm3 .⇒ 44× (R2 - r2) = 99⇒ (R2 - r2) =9/4 = 2.25
4 = 2.25⇒ ( R - r)(R + r) = 2.25
= (0.5)×(R + r) = 2.25
×(R + r) = 2.25R + r = 2.25/0.5 = 4.5
0.5 = 4.5R + r = 4.5 ------------ (2)
0.5 = 4.5R + r = 4.5 ------------ (2)Adding (1) and (2) we get
0.5 = 4.5R + r = 4.5 ------------ (2)Adding (1) and (2) we get2R = 4.5 + 0.5 = 5
0.5 = 4.5R + r = 4.5 ------------ (2)Adding (1) and (2) we get2R = 4.5 + 0.5 = 5∴ R = 2.5 cm and r = 2 cm
0.5 = 4.5R + r = 4.5 ------------ (2)Adding (1) and (2) we get2R = 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.