An open box is to be made from cutting squares of side "s" from each corner of a piece of cardboard 25" by 30".
Write an expression for the volume, V, of the box in terms of s.
-I have no idea where to start on this. I know V=lwh (length*width*height), but what about "s" and the 25x30 piece? I'm so confused. Help please?
Thank you so much! :)
Isn't height s? and length 30-2s, and width 25-2s?
Draw a figure and see.
25x2+ 30x
To find the expression for the volume of a box created by cutting squares of side length "s" from each corner of a piece of cardboard, we need to follow these steps:
1. Start by determining the dimensions of the box after the squares are cut. Since squares of side length "s" are cut from each corner, the new length and width of the cardboard will be decreased by 2s. So, the length and width of the box will be (25 - 2s) and (30 - 2s) respectively.
2. The height of the box will be equal to the side length of the squares that were cut, which is "s".
3. To calculate the volume of the box, use the formula V = lwh. Substitute the values found in step 1 into this formula.
Therefore, the expression for the volume, V, of the box in terms of "s" is:
V = (25 - 2s)(30 - 2s)(s)
Simplifying further, you can multiply the terms to get the final expression:
V = (750 - 50s - 60s + 4s^2)(s)
V = (750 - 110s + 4s^2)(s)
V = 4s^3 - 110s^2 + 750s
So, the expression for the volume, V, in terms of "s" is 4s^3 - 110s^2 + 750s.