Solve for the surface area of the rectangular prism.
• 111 square inches
• 270 square inches
• 222 square inches
• 180 square inches
To solve for the surface area of a rectangular prism, you need to find the sum of the areas of all six sides.
Let's denote the length, width, and height of the rectangular prism as L, W, and H respectively.
The formula for the surface area of a rectangular prism is:
Surface Area = 2(LW + WH + LH)
Given the options, we need to try out different dimensions of the rectangular prism to see which one gives the desired surface area.
Let's start by trying a dimension for the rectangular prism:
L = 6 inches, W = 5 inches, H = 6 inches
Plugging the values into the formula:
Surface Area = 2(6*5 + 5*6 + 6*6)
Surface Area = 2(30 + 30 + 36)
Surface Area = 2(96)
Surface Area = 192 square inches
Since none of the given options match the calculated surface area of 192 square inches, we can conclude that the dimensions we used are incorrect.
Now, let's try another set of dimensions:
L = 6 inches, W = 5 inches, H = 3 inches
Plugging the values into the formula:
Surface Area = 2(6*5 + 5*3 + 6*3)
Surface Area = 2(30 + 15 + 18)
Surface Area = 2(63)
Surface Area = 126 square inches
Since none of the given options match the calculated surface area of 126 square inches, we can conclude that the correct dimensions to achieve a surface area of 111 square inches are not possible.
For the remaining options, we would need to try different dimensions or use a different method to determine the correct surface area.