Question

A rectangular box, half filled holds 180 cubic feet of grain. If the box is 6 feet wide and 3 feet long, how deep is it?

Answer 1

20 feet

Explanation:

Let's start by using the formula for the volume of a rectangular box:

`\sf\qquad\dashrightarrow V = lwh`

where:

• V is the volume
• l is the length
• w is the width
• h is the height

We know that the box is half filled with grain, so the volume of the grain is:

`\sf:\implies V_(grain) = 0.5V = 0.5lwh`

We also know that the volume of the grain is 180 cubic feet, so we can set up an equation:

`\sf\qquad\dashrightarrow 0.5lwh = 180`

We are given that the box is 6 feet wide and 3 feet long, so we can substitute those values in:

`\sf:\implies 0.5(3)(6)h = 180`

Simplifying:

`\sf:\implies 9h = 180`

`\sf:\implies \boxed{\bold{\:\:h = 20\:\:}}\:\:\:\green{\checkmark}`

Therefore, the depth of the box is 20 feet.

Answer 2

Answer: 10

Step-by-step explanation: Volume = length*width*depth. 180 = 6*3*depth. 6*3 = 18. We divide 180 by 18, to get 10. Depth = 10