Edythe C. answered • 07/11/22
Getting the foundation right
This problem wants you to see how surface area and volume are related. Find a die you use in playing a board game. Look at it and notice that all six faces are the same. That's because both sides of a cube face are the same. So instead of saying length times width equals area, we can call any cube side S and write S times S or S^2 equals area. Likewise, volume of a cube is S times S times S or S^3.
We're told that the surface area of our problem cube is 60. Since each face's area is S^2 and there are six of these faces, we can write 6S^2 = 60 and solve for the value of one side or S. Once we know what S is, we can cube that to get volume. The tricky part is solving for S. Get S^2 alone on the left and take the square root of both sides, leaving S as sqrt of something. Then when you cube, remember that sqrt of something times sqrt of something is that something. So your answer is that something times sqrt of something. Have fun!
