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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?

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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