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27 January, 21:08

Item 17 A sphere and a right cylinder have the same radius and volume. Find the radius rr in terms of the height hh of the cylinder.

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  1. 27 January, 21:17
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    Sphere and right cyl. have the same radius and volume. Thus, find the equations for the volumes of a sphere and a right cylinder and set them equal to one another:

    Vol. of sphere = Vol. of right cyl.

    (4/3) pi r^3 = pi r^2 * h

    "pi" appears on both sides of this equation as "pi." So we can cancel "pi" from both sides. We then have:

    (4/3) r^3 = r^2 h

    Let's now divide both sides of this new equation by r^2. We then have:

    (4/3) r = h

    We must solve this for r in terms of h. To do this, multiply both sides of this equation by (3/4). This results in:

    r = (3/4) h This is the final answer: the radius, r, in terms of the height, h.
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