If a metal pipe 10cm long has an external diameter of 12cm and a thickness of 1cm find the volume of the metal used in making the pipe
A
120\(\pi\)cm3
B
110\(\pi\)cm3
C
60\(\pi\)cm3
D
50\(\pi\)cm3
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The volume of the pipe is equal to the area of the cross section and length.
let outer and inner radii be R and r respectively.
Area of the cross section = (R2 - r2)
where R = 6 and r = 6 - 1
= 5cm
Area of the cross section = (62 - 52)\(\pi\) = (36 - 25)\(\pi\)cm sq
vol. of the pipe = \(\pi\) (R2 - r2)L where length (L) = 10
volume = 11\(\pi\) x 10
= 110\(\pi\)cm3
Source: Myschool Past Questions Archive (Record #31768)