Which option expresses the surface area of a rectangular prism with the following dimensions: length = 4, width = 3, height = 6 ?
A
(4 × 3 + 4 × 6 + 3 × 6)
B
2 (4 × 3 + 4 × 6 + 3 × 6)
C
2 ( 4 × 3 × 6)
D
2 ( 4 + 3 + 6)
The correct option is B: 2 (4 × 3 + 4 × 6 + 3 × 6).
The surface area of a rectangular prism is calculated by adding up the areas of all the faces. Since a rectangular prism has 6 faces, we need to calculate the area of each pair of opposite faces and then add them up.
The formula for the surface area of a rectangular prism with dimensions length = l, width = w, and height = h is:
2lw + 2lh + 2wh
Plugging in the given dimensions (l = 4, w = 3, h = 6) into the formula:
2(4*3) + 2(4*6) + 2(3*6)
= 2(12) + 2(24) + 2(18)
= 24 + 48 + 36
= 108
So, the surface area of the rectangular prism is 108.