Question

Question #9154e

Answer 1

`490pi~~1539.38" cubic cm"`

Explanation:

`"the volume of a cylinder is"`

`• " volume "=pir^2h`

`"where r is the radius and h the height"`

`"volume of metal "`

`="volume of cylinder "-" volume of hollow"`

`"internal radius "r_1=24`

`rArr"external radius "r_2=24+1=25`

`"volume of metal "=pir_2^2h-pir_1^2h`

`color(white)("volume of metal ")=pih(r_2^2-r_1^2)`

`color(white)("volume of metal ")=10pi(25^2-24^2)`

`color(white)("volume of metal ")=10pixx49`

`color(white)("volume of metal ")=490pi~~1539.38`

Answer 2

`490pi color(white)(.)cm^3` as an exact answer

Explanation:

In this case the volume is surface area of the metal at the end (green) times the length of the tube.

Consider the end (cross section)

If we subtract the cross section area of the hollow from the whole we have the area of the green part. Which is what we need.

Radius form the centre to the outside is `24+1=25 cm`

`color(brown)("Note that the area of a circle is "pir^2" where "r" is the radius")`

Area of the whole - area of the 'hollow' = area of metal

# color(white)("dddd")pi25^2color(white)("ddddd") - color(white) ("ddddd")pi24^2color(white)("dddd")=color(white)("ddd")49pi color(white)(.)cm^2#

The length of the tube is `10cm`

`"Area "xx" length = volume"`
`color(white)("d")49picolor(white)("d.")xxcolor(white)("ddd")10color(white)("d")=color(white)("d")490pi`

But volume is in `cm^3` so we have `490picm^3` as an exact answer