Squares of side a are cut from each corner of a 8 in X 6 in rectangle so that it's sides can be folded to make a . Represent function in terms of a that can be define the volume of the box
v = x(8-2x)(6-2x)
V(a)= 4a3 - 28a2 +48a
Answer
V(a) =47a - 28a² +4a³
To find the volume of the box that can be formed by cutting out squares from each corner of a rectangle, we need to consider the dimensions of the resulting box.
Let's say the length of the rectangle is L and the width is W. In this case, L = 8 in and W = 6 in.
By cutting squares of side a from each corner, we are essentially reducing the length by 2a (as we are cutting from both ends) and reducing the width by 2a as well.
The resulting dimensions of the box will be:
- Length: L - 2a
- Width: W - 2a
- Height: a
Therefore, the volume of the box can be calculated as:
Volume = (L - 2a) * (W - 2a) * a
In the given function, we can substitute the specific values of L and W, or we can use the variables L and W to represent any specific values. The function in terms of 'a' then becomes:
Volume = (8 in - 2a) * (6 in - 2a) * a