A cylinder pipe made of metal is 3cm thick, if the internal radius of the pipe is 10cm, find the volume of metal used in making 3m of the pipe.
If a cylindrical pipe made of metal is 3cm thick, and the internal radius of the pipe is 10cm, the volume of metal used in making 3m of the pipe is = 20,700πcm³.
Internal radius = 10cm
External radius = 10 + thickness = 10 + 3 = 13cm
Recall that the volume of a cylinder = πr²h
Where r = radius, and
h = height of the cylinder = length of the pipe = 3m = 300cm.
Thus, the volume of the metal used in making the pipe = volume of external cylinder – volume of internal cylinder.
Volume of external cylinder = π × 13² × 300
Volume of external cylinder = 50,700πcm³
Volume of internal cylinder = π × 10² × 300
Volume of internal cylinder = 30,000πcm³
Volume of metal = volume of external cylinder – volume of internal cylinder
= 50,700π – 30,000π
= (50,700 – 30,000)π
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is not correct.
- C is incorrect.
- D is the correct answer.
You may please note these/this:
- The volume of the metal used to make the cylinder will be derived from subtracting the volume of the internal cylinder from the volume of the external cylinder.
- Volume of a cylinder = πr²h.
- You must convert the unit of the length of the pipe from 3m to 300cm. this is to maintain consistency in units since other parameters are given in cm and not in m.
If you love our answers, you can simply join our community and also provide answers like this, fellow learners like you will appreciate it.
/ culled from 2021 JAMB-UTME MATHEMATICS question 20 /