# 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?

Jul 11, 2018

The depth of the trough is $\text{0.2611 ft}$ or $\text{3.1332 in}$.

#### Explanation:

$\text{Volume"="length"xx"width"xx"height}$

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")

$\text{height"=(9.4"ft"^3)/(36"ft"^2)="0.2611 ft}$

Convert feet to inches.

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

Jul 11, 2018

$0.26$ 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

$V = L \cdot W \cdot H$

So the volume of water in the trough is

${V}_{\text{trough}} = 12 \cdot 3 \cdot H$ cubic feet

If ${V}_{\text{trough}} = 9.4$ cubic feet then

$9.4 = 12 \cdot 3 \cdot H$

$\frac{9.4}{12 \cdot 3} = H$

$H = \frac{9.4}{36}$

$H = \frac{9.4}{36}$

$= 0.26$ ft