SajjadAhmad wrote:

A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6

B. 12

C. 15

D. 30

E. 48

The question comes down to determining how to orient the box. Do, we make the HEIGHT of the box 12 inches, 18 inches or 10 inches?

Well, since the height of each CAN is 5 inches, we can see that making the HEIGHT of the box 10 inches is a great course of action. Otherwise, there will be empty space above the cans.

Also, if the radius of each can is 3 inches, then the DIAMETER = 6 inches

So, we want the base of the box to be such that we can fit as many 6-inch diameters into it.

Since 12 inches and 18 inches are both multiples of 6 inches, we can maximize the number of cans by making the 12-inch by 18-inch part of the box the base.

Since with a 12-inch by 18-inch base, we can place 3 rows of 2 cans on the base. This is a total of 6 cans (so far)

Then, we can place a second level of 6 cans on top of the first 6 cans.

So, the most cans we can place in the box = 6 + 6 = 12

Answer: B

Cheers,

Brent

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