Question

How deep is the water in the trough if a water trough is in the shape of a rectangular prism that is 12 feet long by 3 feet wide and has 9.4 cubic feet of water?

Answer 1

The depth of the trough is `"0.2611 ft"` or `"3.1332 in"`.

Explanation:

`"Volume"="length"xx"width"xx"height"`

To calculate height (depth), divide the given volume by the product of the length and width.

`"height"=(9.4"ft"^3)/(12"ft"xx"3ft")`

`"height"=(9.4"ft"^3)/(36"ft"^2)="0.2611 ft"`

Convert feet to inches.

`0.2611color(red)cancel(color(black)("ft"))xx("12 in")/(1color(red)cancel(color(black)("ft")))="3.1332 inches"`

Answer 2

`0.26` ft

Explanation:

A rectangular prism is a 3D shape with 6 faces, where each face is a rectangle.
A rectangle has 4 sides where all 4 corners are right angles (a square is a rectangle with all sides the same length).

The volume of a rectangular prism is length * width * height

`V = L * W * H`

So the volume of water in the trough is

`V_"trough" = 12 * 3 * H` cubic feet

If `V_"trough" = 9.4` cubic feet then

`9.4 = 12 * 3 * H`

`9.4/ (12 * 3)= H`

`H= 9.4/ 36`

`H= 9.4/ 36`

`= 0.26` ft