OG: The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters

[AbeNeedsAnswers]

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly ½ centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum value?

A. 3.5
B. 4
C. 4.5
D. 5
E. 5.5

C

[Jay@ManhattanReview]

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly ½ centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum value?

A. 3.5
B. 4
C. 4.5
D. 5
E. 5.5

C

Given that each side of the cardboard is 1/2 cm thick, the inner dimensions of the cardboard are 7 cm by 9 cm by 11 cm.

Since we want the maximum value of the radius, we must have the height of the cylinder = 7 cm (minimum dimension). Thus, the base of the cardboard = 9 cm by 11 cm. Since the base of the cylinder is circular, the minimum of the two dimensions (9cm and 11 cm) would be its diameter.

Thus, the maximum value of the radius = 9/2 = 4.5 cm

The correct answer: C

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly ½ centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum value?

A. 3.5
B. 4
C. 4.5
D. 5
E. 5.5

C

We see that each of the inner dimensions of the box is 2 x ½ = 1 cm less than its respective outer dimension. Therefore, the inner dimensions of the box are 7 cm by 9 cm by 11 cm. Since the canister has to be able to stand upright when the box rests on one of its sides, the maximum value if the canister’s radius is 4.5 cm (notice that would make the diameter = 9 cm, equaling the smaller of the dimensions of the base of the box if the base is 9 cm by 11 cm and height is 7 cm).

Answer: C