Question 5

Geometry Level 2

A square measure 6 6 centimeters on each side. A square with side length 1.5 1.5 centimeters is cut from each corner. The sides of the new figure are folded up to form a box. The number of cubic centimeters in the volume of the box formed is equal to A B \frac{A}{B} for positive coprime A A and B . B. Find A + B . A+B.


The answer is 29.

Trevor B. by Trevor B. , 22, USA

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2 solutions

Trevor B.
May 25, 2014

The side length of the square base of the box is 6 − ( 1.5 × 2 ) = 6 − 3 = 3 cm . 6-(1.5\times2)=6-3=3\text{ cm}. The height of the box is the amount that was folded up, which is 1.5 cm . 1.5\text{ cm}. The volume of the box is 3 × 3 × 1.5 cm 3 = 13.5 cm 3 = 27 2 cm 3 , 3\times3\times1.5\text{ cm}^3=13.5\text{ cm}^3=\dfrac{27}{2}\text{ cm}^3, so A = 27 A=27 and B = 2 , B=2, and A + B = 29 . A+B=\boxed{29}.

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V = 3 × 3 × 1.5 = 13.5 = 27 2 V=3\times 3 \times 1.5 = 13.5 = \dfrac{27}{2}

Finally, A + B = 72 + 2 = A+B=72+2= 29 \boxed{29}

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