Princeton Review
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
OA B.
A rectangular box, with dimesions of 12 inches by 18 inches
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- Brent@GMATPrepNow
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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?AAPL wrote:Princeton Review
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
OA B.
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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- Scott@TargetTestPrep
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AAPL wrote:Princeton Review
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
OA B.
Notice that each cylinder will take up an area of 6 x 6 = 36 square inches on the base of the box, even though the base area of each cylinder is less than that. Therefore, we can think of the soup cans as 6 x 6 x 5 rectangular boxes instead of cylinders. If the big box is laid on the 12 x 18 base, there will be 12/6 = 2 rows of cans and 18/6 = 3 columns of cans; totaling 2 x 3 = 6 cans on the base. Since the height is 10, 10/5 = 2 cans be stacked; therefore 6 x 2 = 12 cans is the maximum number to fit in the box.
Answer: B
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