A cone with volume 5000 m³ is dilated by a scale factor of 15. What is the volume of the resulting cone? Enter your answer in the box.

Question

A cone with volume 5000 m³ is dilated by a scale factor of 15. What is the volume of the resulting cone? Enter your answer in the box. m³

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Answers ( No )

    0
    2021-09-10T06:22:01+00:00

    The answer is 40, I just took the test.

    0
    2021-09-10T06:22:06+00:00

    Answer:

    40\ m^{3}

    Step-by-step explanation:

    we know that

    If two figures are similar then the ratio of its volumes is equal to the scale factor elevated to the cube

    Let

    z—–> scale factor

    x—–> the volume of the dilated cone

    y—–> the volume of the original cone

    z^{3}=\frac{x}{y}

    In this problem we have

    z=1/5

    y=5,000\ m^{3}

    substitute and solve for x

    (1/5)^{3}=\frac{x}{5,000}

    (1/125)=\frac{x}{5,000}

    x=5,000/125=40\ m^{3}

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