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Volume

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  • A manufacturer made cylindrical containers in heights ranging from 2 feet to 6 feet.
    A customer wanted a container with a 3-foot diameter and a volume, V, of at least 35 cubic feet. This relationship is shown by the inequality

    πr2h = V

    where r is the radius and h is the height. Which is the smallest standard height the
    manufacturer can supply and meet the customer's volume requirements? [Use 3.14
    for p].


    2 ft
    3 ft

    4 ft
    5 ft


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  • The right circular cylinder represented has a base radius of 3 centimeters and a height of 12 centimeters.

    What is the volume of the right circular cylinder in cubic centimeters?


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  • A 30-inch by 50-inch rectangular gate is strengthened by a diagonal wire AB, which connects two opposite corners of the gate as indicated in the figure shown. 

    AB, which connects two opposite corners of the gate as indicated in the figure shown. 

    Which is closest to the length of AB?

    AB?

    40 in.

    58 in.

    68 in.

    80 in.


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  • Matthew took a 10-inch by 10-inch square piece of cardboard and cut an x-inch by x-inch square off each corner. If he folds up the sides to make an open box, which expression represents its volume?

    x2(40 – 8x)
    x(40 – 8x)2
    x2(10 – 2x)
    x(10 – 2x)2


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  • If the volume of a swimming pool is 1,920 cubic feet, and it is 8 feet deep and 20 feet long, how wide is the pool?

    12 feet
    68.5 feet
    1,760 feet
    1,892 feet


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  • You are building a staircase like the one shown that’s 4 steps high. How many cubes would it take to build a staircase that is 12 steps high?

    24
    42
    78
    120


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