Ken is going to build a tree house for his son's 12th birthday. He has 28 meters squared of wood with which to build it. He plans to build it in the shape of a square based prism. How much additional volume can be added to the tree house if Ken leaves the back wall open ( the one against the tree).
To find the additional volume that can be added to the tree house if the back wall is left open, we first need to calculate the volume of the entire tree house and then subtract the volume of the tree house with the back wall closed.
1. Find the volume of the entire tree house:
Since the tree house is in the shape of a square-based prism, we can calculate its volume by multiplying the area of the base (which is a square) by the height.
a. Calculate the length of each side of the square base:
Since it is a square, all sides are equal in length.
Let's assume each side has a length of 'x'.
b. Calculate the area of the base:
The area of a square is given by the formula A = side * side.
In this case, A = x * x = x^2.
c. Calculate the volume of the entire tree house:
Let's assume the height of the tree house is 'h'.
The volume of the prism is given by the formula V = base area * height.
Substituting the values we found:
V = x^2 * h.
2. Find the volume of the tree house with the back wall closed:
Since the back wall is closed, the tree house has two identical square bases and four rectangular faces.
The volume can be calculated by multiplying the area of one base by the height.
a. The area of one square base is x^2 (calculated in the previous step).
b. The height of the tree house remains 'h'.
c. Calculate the volume of the tree house with the back wall closed:
V_closed = x^2 * h.
3. Find the additional volume:
The additional volume is the difference between the volume of the entire tree house and the volume of the tree house with the back wall closed.
Additional volume = V - V_closed.
Now, you need to provide the values of the dimensions (base length and height) to complete the calculation.