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Math Help - Finding radius of the sphere

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    Finding radius of the sphere

    Question: A sphere has the same numerical value for both its surface area and its volume. Find the radius of the sphere.

    My solution: 4πr^2 = 4/3πr^3 but the question say it has to be numerical value. And that is where I got stuck at. Can you explain it to me?
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    Re: Finding radius of the sphere

    First, divide both sides by r^2

    What do you get?
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    Re: Finding radius of the sphere

    Quote Originally Posted by stevecowall View Post
    Question: A sphere has the same numerical value for both its surface area and its volume. Find the radius of the sphere.

    My solution: 4πr^2 = 4/3πr^3 but the question say it has to be numerical value. And that is where I got stuck at. Can you explain it to me?
    \displaystyle \begin{align*} 4\pi r^2 &= \frac{4}{3}\pi r^3 \\ \pi r^2 &= \frac{1}{3}\pi r^3 \\ r^2 &= \frac{1}{3}r^3 \\ 0 &= \frac{1}{3}r^3 - r^2 \\ 0 &= r^2\left(\frac{1}{3}r - 1\right) \\ r^2 = 0 \textrm{ or }\frac{1}{3}r - 1 &= 0 \\ r = 0 \textrm{ or } r &= 3 \end{align*}

    So the radius is either 0 units or 3 units in length.
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    Re: Finding radius of the sphere

    Quote Originally Posted by pickslides View Post
    First, divide both sides by r^2

    What do you get?
    What if r = 0?
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    Re: Finding radius of the sphere

    Quote Originally Posted by Prove It View Post
    What if r = 0?
    It wouldn't be a sphere
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    Re: Finding radius of the sphere

    Quote Originally Posted by pickslides View Post
    It wouldn't be a sphere
    A single point is still a sphere.

    Just like a linear function is a quadratic function, just with a = 0...

    Don't exclude degenerates
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    Re: Finding radius of the sphere

    Does a single point have a non zero surface area and non zero volume? If so can it have a zero radius?
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    Re: Finding radius of the sphere

    Quote Originally Posted by pickslides View Post
    Does a single point have a non zero surface area and non zero volume? If so can it have a zero radius?
    Why do you insist on non zero volume and surface area?
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    Re: Finding radius of the sphere

    Quote Originally Posted by stevecowall View Post
    Question: A sphere has the same numerical value for both its surface area and its volume. Find the radius of the sphere.

    My solution: 4πr^2 = 4/3πr^3 but the question say it has to be numerical value. And that is where I got stuck at. Can you explain it to me?
    n = pi, r = radius

    4nr^2 = 4/3nr^2

    Divide both sides by r^2

    4n = 4/3nr

    Divide by n

    4 = 4/3r

    Divide by 4/3

    4/(4/3) = r

    r = 3

    The radius of the sphere is 3.
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    Re: Finding radius of the sphere

    Quote Originally Posted by okokjae View Post
    n = pi, r = radius

    4nr^2 = 4/3nr^2

    Divide both sides by r^2

    4n = 4/3nr

    Divide by n

    4 = 4/3r

    Divide by 4/3

    4/(4/3) = r

    r = 3

    The radius of the sphere is 3.
    You can't divide by r^2 because you don't know for sure that r =/= 0.
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