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Math Help - Volume of a sphere

  1. #1
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    Volume of a sphere

    The volume of a sphere is proportional to the cube of its radius. Sphere A has volume V and radius R. The radius of Sphere B is twice the radius of Sphere A. Find the volume of Sphere B.

    How would I go about doing this? Would the formula of a sphere even be needed?

    Thanks for all help!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Intrusion View Post
    The volume of a sphere is proportional to the cube of its radius. Sphere A has volume V and radius R. The radius of Sphere B is twice the radius of Sphere A. Find the volume of Sphere B.

    How would I go about doing this? Would the formula of a sphere even be needed?

    Thanks for all help!
    V_a=\frac{4}{3}\pi{r^3}

    V_b=\frac{4}{3}\pi(2r)^3
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  3. #3
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    So then, the volume of sphere B will be 8V, correct? :P
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  4. #4
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    You can use the sphere volume formula,

    or you can simply say

    V_A=kR^3

    V_B=k(2R)^3=k2^3R^3=8kR^3

    Whatever the volume of sphere A,
    sphere B will be 8 times that.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Intrusion View Post
    So then, the volume of sphere B will be 8V, correct? :P
    Yes,, the volume of shpere B will be 8 times that of sphere A, or

    8V_a=V_b
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  6. #6
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    And notice that once you were told "The volume of a sphere is proportional to the cube of its radius" you did not need the actual formula for the volume. The radius was multiplied by 2 so the volume is multiplied by 2^3= 8.
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