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 Question from Jenesis, a student: For Awards Night at Baddeck High School, the math club is designing small solid silver pyramids.The base of the pyramids will be a 2 in by 2 in square. The pyramids should not weigh more than 2.5 pounds. One cubic foot of silver weighs 655 pounds. What is the maximum height of the pyramids?

Hi Jenesis,

I would guess that the height is less than a foot so I work in inches. Since there are 12 inches in a foot there are $12 \times 12 \times 12 = 1728$ cubic inches in a cubic foot and hence a cubic inch of silver weighs $\large \frac{655}{1728} \normalsize = 0.3791$ pounds.

Let the height of the pyramid be $h$ inches. The volume $V$ of a pyramid is given by

$V = \frac13 \times \mbox{(the area of the base)} \times \mbox{ (the height).}$

Write the volume of your pyramid in cubic inches in terms of $h.$ What will this volume weigh? If this weight is 2.5 pounds solve for $h.$

Penny

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