Answer:
To find the volume of a rectangular prism, we need to know the dimensions of all three sides. In this case, we are given two side lengths, 11ft and 4ft, and the surface area of the prism, which is 268ft².
Let's assume that the length of the rectangular prism is L, the width is W, and the height is H. We can set up equations based on the given information to solve for these variables.
The formula for the surface area of a rectangular prism is:
2(LW + LH + WH) = 268ft²
Since we know two side lengths, we can substitute them into the equation:
2(11ft * 4ft + 11ft * H + 4ft * H) = 268ft²
Simplifying this equation gives us:
88ft + 15H = 134ft²
Now we can solve for H by isolating it on one side of the equation:
15H = 134ft² - 88ft
15H = 46ft²
H = 46ft² / 15
H ≈ 3.067 ft
Now that we have found the height of the rectangular prism, we can calculate its volume using the formula:
Volume = Length * Width * Height
Volume = 11ft * 4ft * 3.067 ft
Volume ≈ 133.874 ft³
Therefore, the volume of the rectangular prism is approximately 133.874 ft³.
Explanation: