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8 November, 11:09

Celeste made 6 cone shaped ice blocks that each have a radius of 2.8 in. and a height of 7 in. She used a cylindrical container with a radius of 9 in. to fill all of the cones. What is the height of the cylindrical container? Use 3.14 to approximate pi and round your answer to two decimals places. show your work.

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  1. 8 November, 13:00
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    Volume (cone) = (1/3) (b x h)

    b=base

    h=height

    1) we calculate the total volume of the 6 cones:

    Total volume of the 6 cones.=6 (1/3) (b x h=2 (b x h)

    base: πr²=π (2.8 in) ²=7.84 in²

    Total volume=2 (7.84π in² * 7 in) = 109.76π in³

    2) we calculate the Volume of the cylindrical container.

    Volume (cylinder) = base * height

    base=πr²=π (9 in) ²=81π in²

    Volume = (81π in² * h) = 81πh in²

    Therefore:

    Volume of the 6 cones = volume of the cylinder

    109.76π in³=81πh in²

    h = (109.76π in³) / (81π in²) = 1.3550 in≈1.36 in

    Answer: The height is 1.36 in.
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