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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?

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 class=

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twvogels
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. 

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