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Math Help - Is my answer correct?

  1. #1
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    Is my answer correct?

    A sphere inscribes a cube of the side length 10 mm. What is the volume and surface area of the sphere?

    My answer is 1333.33333 pie mm cubbed. is it right?
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  2. #2
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    Quote Originally Posted by yitsongg View Post
    A sphere inscribes a cube of the side length 10 mm. What is the volume and surface area of the sphere?

    My answer is 1333.33333 pie mm cubbed. is it right?

    HI

    I don think so .

    The formula of sphere is 4/3 pi r^3

    You substituted 10 which is the diameter into r .

    THe correct one should be 4/3 pi (5)^3 for volume

    and 4 pi (5)^2 for surface area
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  3. #3
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    Quote Originally Posted by yitsongg View Post
    A sphere inscribes a cube of the side length 10 mm. What is the volume and surface area of the sphere?

    My answer is 1333.33333 pie mm cubbed. is it right?
    If a sphere inscribes a cube then the cube is INSIDE the sphere.
    If a sphere is inscribed in a cube then the cube is OUTSIDE the sphere.


    If the cube is INSIDE the sphere and has side length of 10, then the diameter of the cube will equal the diameter of the sphere.

     \sqrt{ 10^2 + 10^2 + 10^2 } = 17.3205

    The sphere radius is 8.66

    The Volume of the sphere
     V = \dfrac{4}{3} \pi r^3 = 2720.7

    ...................

    If the sphere is INSIDE the cube which has side lengths of 10, then the diameter of the cube will equal the side length of the cube.

    The sphere radius is 5.00

    The Volume of the sphere
     V = \dfrac{4}{3} \pi r^3 = 523.6

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