Question

The water supply uses huge concrete pipes to drain stormwater.

a Find the external radius of a pipe.

b Find the Internal radius of a pipe.

c Find the volume of concrete necessary to make one pipe.
​

Answer 1

a. External radius is 0.5 m.

b. Internal radius is 0.45 m.

c. Volume of concrete necessary to make one pipe is 0.37
`m^(3)`.

Explanation:

a. It can be observed that the diameter of the pipe is 1 m.

External radius =
`(diameter)/(2)`

=
`(1)/(2)`

= 0.5

External radius = 0.5 m

b. Internal radius of the pipe can be determined by;

Internal radius =
`(internal diameter)/(2)`

But,

Internal diameter = 1 m - (2 x 0.05 m)

= 1 m - 0.10 m

= 0.9 m

Internal diameter = 0.9 m

So that,

Internal radius =
`(0.9)/(2)`

= 0.45

Internal radius = 0.45 m

c. Volume of concrete required =
`\pi`
`r_(e) ^(2)`h -
`\pi`
`r_(i) ^(2)`h

where
`r_(e)` is the external radius, and
`r_(i)` is the internal radius.

Volume of concrete required = [
`(22)/(7)` x
`(0.5)^(2)` x 2.5] - [
`(22)/(7)` x
`(0.45)^(2)` x 2.5]

= 1.9643 - 1.5911

= 0.3732

The volume of concrete necessary to make one pipe is 0.37
`m^(3)`.