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27 October, 03:09

Anders is using casts to make plaster figures. He has a cylinder cast that has a diameter of 8 inches and

is 24 inches tall. Anders uses a cone-shaped container with a diameter of 12 inches and a height of

16 inches to fill his casts. How many cone-shaped containers full of plaster will he need to completely fill

the cylinder cast?

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The given cylindrical container is used to fill the rectangular prism fish tank with water.

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Answers (1)
  1. 27 October, 03:29
    0
    Two cone-shaped containers will be needed

    Step-by-step explanation:

    The key to finding the answer to this is to calculate the volumes of each of the shapes.

    For the cylinder cast, the volume will be π * r^2 * h, where r is D/2 = 8/2 = 4 inches and h = 24 inches

    V = π * 4^2 * 24 = 384 π inches^3

    For the cone-shaped container, its volume is 1/3 * π * r^2 * h

    where r is D/2 = 12/2 = 6 inches and h is 16 inches

    The volume = 1/3 * π * 6^2 * 16 = 192 π inches^3

    Thus, the number of cone-shaped containers needed to fill the casting will be the volume of the casting divided by the volume of the container

    = 384 π / 192 π = 2
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