This is the top view (and mat plan) of a rectangular prism made of 1 cm³ blocks:
a) What is its surface area in cm²? b) What is its volume in cm³?
a) To find the surface area, we need to add up the area of each face. There are 2 faces that are length x width, and 2 faces that are length x height, and 2 faces that are width x height. The length is 10 blocks, the width is 8 blocks, and the height is 6 blocks. So the surface area is:
SA = 2lw + 2lh + 2wh
SA = 2(10)(8) + 2(10)(6) + 2(8)(6)
SA = 160 + 120 + 96
SA = 376 cm²
b) To find the volume, we need to multiply the length, width, and height. The length is still 10 blocks, the width is 8 blocks, and the height is 6 blocks. So the volume is:
V = lwh
V = 10 x 8 x 6
V = 480 cm³