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Hello, I am having to take developmental pre algebra at the college level. Can you help me answer a few questions?

One problem in my text goes something like this (not the exact wording but close): A toy baseball bat comes with 3 balls in a box which is a rectangular solid. The box is big enough to hold only the 3 balls which have a radius of 1.3 inches. What is the volume of air in the box surrounding the balls?

Another that I am having problems with is this: How high would a tree be that casts a 37 foot shadow at the same time a 70 foot flagpole casts a 50 foot shadow. Round your answers to the nearest 10th.

Thank you in advance.

So the box has to be 2.6 inches wide, 2.6 inches high and 7.8 inches long which makes the volume of the box 52.728 cubic inches.  Each ball has a volume of (4/3)(pi)(1.3)^3 = 9.203 cubic inches so three balls have a volume of 27.608 cubic inches.  The volume of air is the difference, 25.12 cubic inches.

This is a simple ratio, 70/50 = x/37 so x = 51.8 ft


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