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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.

User Radarek
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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.
User George Richardson
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