A hole shaped like a rectangular prism is 3 feet wide, 5 feet long, and 3 feet deep. If the hole is made 2 feet deeper, how much will the volume of the hole increase?
V=45+2= 47
3*5*3 = 45
3*5*5 = 75
that is 30 more cubic feet
To find the increase in volume of the hole when it is made 2 feet deeper, we need to calculate the volume of the hole before and after the change and then find the difference between the two volumes.
The volume of a rectangular prism can be calculated by multiplying its length, width, and depth.
Before the change, the dimensions of the hole are:
Width = 3 feet
Length = 5 feet
Depth = 3 feet
So, the initial volume of the hole is:
Volume_before = Width * Length * Depth = 3 ft * 5 ft * 3 ft = 45 cubic feet
After the change, the depth of the hole increases by 2 feet. So, the new depth is:
New Depth = Initial Depth + Change in Depth = 3 ft + 2 ft = 5 ft
The dimensions of the hole after the change are still the same in terms of width and length.
So, the new volume of the hole is:
Volume_after = Width * Length * New Depth = 3 ft * 5 ft * 5 ft = 75 cubic feet
The increase in volume is the difference between the new volume and the initial volume:
Increase in volume = Volume_after - Volume_before = 75 cubic feet - 45 cubic feet = 30 cubic feet
Therefore, the volume of the hole will increase by 30 cubic feet when it is made 2 feet deeper.