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: [tex] V=lwh = 48 \times 24 \times 24 = 48 \times 24^{2}[/tex]
Volume of two balls: [tex] V = 2(\frac{4}{3} \pi r^{3}) = 2(\frac{4}{3} \pi \times 12^{3})[/tex]
Total volume = box - balls: [tex]V_{total}=48 \times 24^{2} - 2(\frac{4}{3} \pi \times 12^{3})[/tex]
This matches A, just as we thought.
