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?
To find the surface area of each prism, we need to calculate the surface area of each face and then add them together.
For Prism A:
Surface Area = 2(2x3 + 3x4 + 2x4)
Surface Area = 2(6 + 12 + 8)
Surface Area = 2(26)
Surface Area = 52 cm^2
For Prism B:
Surface Area = 2(4x6 + 6x8 + 4x8)
Surface Area = 2(24 + 48 + 32)
Surface Area = 2(104)
Surface Area = 208 cm^2
Now, to find out how many times the surface area of Prism B is compared to Prism A, we 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.