Question
The dimensions for two rectangular prisms are shown below.
Prism A: 2 cm by 3 cm by 4 cm
Prism B: 4 cm by 6 cm by 8 cm
The surface area of prism B is how many times the surface area of prism A?
A.
3 times
B.
8 times
C.
2 times
D.
4 times
Prism A: 2 cm by 3 cm by 4 cm
Prism B: 4 cm by 6 cm by 8 cm
The surface area of prism B is how many times the surface area of prism A?
A.
3 times
B.
8 times
C.
2 times
D.
4 times
Answers
GPT 3.5
D. 4 times
To find the surface area of a rectangular prism, you need to calculate the sum of the areas of all six faces.
Surface area of Prism A = 2(2x3 + 3x4 + 2x4) = 2(6 + 12 + 8) = 2(26) = 52 cm^2
Surface area of Prism B = 2(4x6 + 6x8 + 4x8) = 2(24 + 48 + 32) = 2(104) = 208 cm^2
To find out how many times the surface area of Prism B is compared to Prism A, you divide the surface area of Prism B by the surface area of Prism A:
208 cm^2 / 52 cm^2 = 4
Therefore, the surface area of Prism B is 4 times the surface area of Prism A.
To find the surface area of a rectangular prism, you need to calculate the sum of the areas of all six faces.
Surface area of Prism A = 2(2x3 + 3x4 + 2x4) = 2(6 + 12 + 8) = 2(26) = 52 cm^2
Surface area of Prism B = 2(4x6 + 6x8 + 4x8) = 2(24 + 48 + 32) = 2(104) = 208 cm^2
To find out how many times the surface area of Prism B is compared to Prism A, you divide the surface area of Prism B by the surface area of Prism A:
208 cm^2 / 52 cm^2 = 4
Therefore, the surface area of Prism B is 4 times the surface area of Prism A.