Problem 14
<h3>Answer: They bought <u>too much</u> sand</h3>
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Explanation:
Because the sandbox is a rectangular prism, aka a block, we multiply the length width and height to get the volume.
Volume = length*width*height = 6*5*1.2 = 36
The volume of the sandbox is 36 cubic feet.
The customer bought 40 cubic feet of sand, which exceeds the volume we computed earlier. The customer bought <u>too much</u> sand.
If it was a choice of buying too much or too little, I think it's better to go overboard just so you don't have to return to the store. The extra amount of sand (40-36 = 4 cubic feet) can possibly sold or donated at a later time.
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Problem 15
<h3>Answers:</h3>
- The equation could be 306.52 = 19.4h or 19.4h = 306.52
- Either equation mentioned solves to h = 15.8; so the height of the prism is 15.8 meters
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Explanation:
The rectangular prism formula to calculate the volume is
Volume = length*width*height
Note that the portion "length*width" can be replaced with "base area", because the base area is a rectangle.
So we can have this alternative formula
Volume = (base area)*height
If we know the area of the floor, and multiply by the height of the wall, then we can calculate the volume of a room like this. In this case, the floor is 19.4 square meters in area. The overall room is 306.52 cubic meters. We'll let h be the height of the wall. Use algebra to solve for h
Volume = (base area)*height
306.52 = 19.4h .... is one equation to set up
19.4h = 306.52
h = 306.52/19.4
h = 15.8
We divide both sides by 19.4 to undo the multiplication going on.
The height of the prism is 15.8 meters.
