Geometry Word Problem, help ASAP

Question

Max is painting four 20 foot tall palm trees alongside his house. Each tree will need a cylindrical hole that is 34 inches in diameter and 28 inches deep to accommodate the roots. His trash hauler will only take away the excess dirt if it is in rectangular bags that are 2 feet by 1.5 feet by four feet. However, Max can only fill the bags one third of the way or they will be too heavy for him to move. How many bags will he have to buy so he can put all the dirt out for pickup?

 

A. 5

B. 15

C. 24

D. 59

Answer 1

The height of the trees doesn't matter. the volume of a cylinder is (pi)(r^2)(h) (the area of the circle times the height).  For each tree, that's 17 squared (radius is half of the diameter) times 28 cubic inches, or 8,092 cubic inches.  That's a total of 32,368 cubic inches (since there are 4 trees).

 

Each bag holds (24)(18)(48) cubic inches of dirt (changing feet to inches by multiplying each dimension by 12), or 20,736 cubic inches.  But only 1/3 of them is usable, so that's 6,912 cubic inches.  To figure out the number of bags, divide the total amount of dirt (32,368) by the amount of dirt each bag holds (6,912).  That doesn't come out evenly, but it doesn't have to - it's bigger than 4, but smaller than 5, so four bags won't do it, but five will.  (A) is correct.