Question

Help me find the volume?

My teacher requires work being shown, if it is not too much of a hassle. Please show work!!! Thank you!!!!

Answer 1

The volume of the shape is `36` square feet.

Explanation:

No problem at all, Nissa.

The shape shown above is a cuboid with a hole that is also a cuboid. so the total volume will be the volume of the larger cuboid minus the volume of the smaller cuboid.

The formula for volume of a cuboid is:

`V=lxxbxxh` where `l=`length, `b=`breadth and `h=`height.

We start with the larger cuboid (`lc`).

`Vlc=4xx3xx4`

`Vlc=48`

So the volume of the larger cuboid is `48` square feet.

Now we calculate the volume of the hole or the smaller cuboid (`sc`).

`Vsc=2xx3xx2` The width is the same as that of the larger cuboid.

`Vsc=12`

So the volume of the smaller cuboid is `12` square feet.

The volume of the shape (`V`) will be the difference between the two volumes (`Vlc-Vsc`).

`V=48-12`

`V=36`

The volume of the shape is `36` square feet.