# A cylinder pipe made of metal is 3cm thick…

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A. 153πcm3

B. 207πcm3

C. 15,300πcm3

D. 20,700πcm3

D

## DETAILS…

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.

### Data given:

External radius = 10 + thickness = 10 + 3 = 13cm

Recall that the volume of a cylinder = πr²h

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

Thus,

Volume of metal = volume of external cylinder – volume of internal cylinder

= 50,700π – 30,000π

= (50,700 – 30,000)π

= 20,700πcm³

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is not correct.
3. C is incorrect.
4. D is the correct answer.

## KEY-POINTS…

• 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.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 20 /

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