To find the dimensions of a rectangular prism with a surface area greater than 140 square feet, we can calculate the surface area of each given option. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
Let's calculate the surface area for each given option:
1. 6 feet by 2 feet by 3 feet:
Surface Area = 2(6)(2) + 2(6)(3) + 2(2)(3) = 24 + 36 + 12 = 72 square feet
2. 6 feet by 5 feet by 4 feet:
Surface Area = 2(6)(5) + 2(6)(4) + 2(5)(4) = 60 + 48 + 40 = 148 square feet
3. 7 feet by 6 feet by 4 feet:
Surface Area = 2(7)(6) + 2(7)(4) + 2(6)(4) = 84 + 56 + 48 = 188 square feet
4. 8 feet by 3 feet by 7 feet:
Surface Area = 2(8)(3) + 2(8)(7) + 2(3)(7) = 48 + 112 + 42 = 202 square feet
5. 8 feet by 4 feet by 3 feet:
Surface Area = 2(8)(4) + 2(8)(3) + 2(4)(3) = 64 + 48 + 24 = 136 square feet
Based on the calculations, the dimensions of the rectangular prism with a surface area greater than 140 square feet are:
- 7 feet by 6 feet by 4 feet (Option 3)
- 8 feet by 3 feet by 7 feet (Option 4)
These two options have surface areas of 188 square feet and 202 square feet, respectively, both exceeding 140 square feet.
