Calc Question: Find Side Length of Cut Squares for 1575 cm^3 Box

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In summary, the problem involves creating an open box by cutting four identical squares from the corners of a sheet of metal 25 cm by 32 cm, and folding up the metal to form sides. The capacity of the box must be 1575 cm^3. The side length of the squares removed is 3.5 cm. To solve word problems, it is important to read the problem slowly and carefully and create a visual representation to clearly understand the problem.
  • #1
Kuja
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I know this is simple, but I don't understand the English of this problem:

An open box, no more than 5 cm in height, is to be formed by cutting four identical squares from the corners of a sheet of metal 25 cm by 32 cm, and folding up the metal to form sides. The capacity of the box must be 1575 cm^3. What is the side length of the squares removed?

Anyone that cares to help or explain this problem will be welcome!
Thanks in advance! :smile:
 
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  • #2
problem makes little sense.
 
  • #3
Well I found the equation to be (32-2x)(25-2x)x=1575
where x = 3.5
But still, if anyone can explain this problem in a more simple format, then I can ensure myself won't be stuck in one of these word problems, it really took me too long to figure this out. Thanks in advance!
 
  • #4
ok, makes sense now- you are cutting squares on the corner
edges of the sheet. Well, you solved the problem , what exactly
do you need help on? The problem is pretty simple once
we understand the instruction. A picture is worth a thousand
words...
 
Last edited:
  • #5
I need help on solving word problems fast. I can solve an algebra mathematical problem like 10X faster than I can solve word problems. Any tips? :smile:
 
  • #6
Well, the key thing is to understand the problem.
I screwed up on your question because I missed
the keyword "corners", reading too rapidly. I thought
the question asked one to cut the metal into 4
squares, lol.

So, read the problems slowly and draw a cartoon diagram
of it, making sure you clearly see what you are solving.
 
Last edited:

FAQ: Calc Question: Find Side Length of Cut Squares for 1575 cm^3 Box

How do you find the side length of cut squares for a 1575 cm^3 box?

To find the side length of cut squares for a 1575 cm^3 box, you will need to use the formula for the volume of a cube. The formula is V = s^3, where V is the volume and s is the side length. In this case, we know that the volume is 1575 cm^3, so we can plug that in for V. This gives us the equation 1575 = s^3. To solve for s, we can take the cube root of both sides, giving us s = 10. Therefore, the side length of each cut square is 10 cm.

What is the unit of measurement for the side length?

The unit of measurement for the side length will be the same as the unit of measurement for the volume, which in this case is cm.

How many cut squares are needed for a 1575 cm^3 box?

To determine how many cut squares are needed, we can use the formula for the surface area of a cube, which is SA = 6s^2, where SA is the surface area and s is the side length. In this case, we know that the volume is 1575 cm^3 and the side length is 10 cm, so we can plug those values into the formula. This gives us SA = 6(10)^2 = 600 cm^2. Therefore, we would need 600 cut squares to make a 1575 cm^3 box.

Can this formula be used for any size box?

Yes, this formula can be used for any size box as long as it is a perfect cube (meaning all sides are equal in length). The volume of a cube is always calculated by taking the side length and cubing it, and the surface area is always calculated by taking the side length and squaring it, then multiplying by 6.

What is the relationship between the volume and the side length of a cube?

The relationship between the volume and the side length of a cube is that the volume is equal to the side length cubed. This means that as the side length increases, the volume will increase exponentially. Similarly, if the volume is known, we can find the side length by taking the cube root of the volume.

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