Question

EASY 5 POINTS!!! This box has the same length, width, and height as the 2 basketballs. Which expression gives the volume of the empty space encircling the basketballs inside the box?

Answer 1

the upper left on TTM Trust

Answer 2

This one is easier to work out by elimination than by actual math:

1. We know it's a difference, therefore we need to subtract the volume of the balls from the volume of the box. B is wrong.

2. The box is 3dimensional so we must have 3 linear measurements multiplied together in it's volume calculation. D is wrong.

3. The sphere volume formula uses radius cubed (not diameter). C is wrong

A is the only one left and must be correct.

To check:
Volume of the box:
`V=lwh = 48 * 24 * 24 = 48 * 24^(2)`

Volume of two balls:
`V = 2((4)/(3) \pi r^(3)) = 2((4)/(3) \pi * 12^(3))`

Total volume = box - balls:
`V_(total)=48 * 24^(2) - 2((4)/(3) \pi * 12^(3))`

This matches A, just as we thought.