Advanced Math/Volume # 2

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Question
A berry container has the following dimensions:

Top- 5 1/4 inches square

Bottom- 4 1/4 inches square

Height- 2 3/4 inches

Calculate volume of the container.  If the container is full (level), will it hold a quart of berries?

Answer
This is similar to the bucket question. Treat the berry container (turned upside-down) as part of a larger object.
The container is a pyramid with the top cut off:
https://www.flickr.com/photos/dwread/14347268630/

Let θ be the slant angle of the sides.
tanθ = 2.75/0.5 = 5.5

height of pyramid = (5.25/2)tanθ = 14.4375 inches.
volume of pyramid = LWH/3 = 5.25²·14.4375/3 = 132.645 in³

volume of smaller pyramid = LWH/3 = 4.25²·(14.4375-2.75)/3 = 70.3685 in³

volume of berry basket = (volume of pyramid) - (volume of smaller pyramid) = 132.645 - 70.3685 = 62.2765 in³
:::::
"If the container is full (level), will it hold a quart of berries?"
1 US quart = 57.75 in³  < 62.2765 in³, so the container will hold a quart of berries.

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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