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# help

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A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar. The volume of the cylinder is 432pi. What is the volume of the sphere?

Mar 24, 2020

#1
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The volume of a cylinder =  pi r^2 h

432 pi = pi r^2 h    divide both sides by pi

432 = r^2 h            Now since the ball touches the bottom and top    and the sides

h must be equal to diameter    and thus r = h/2   put this into the equation

432 = (h/2)^2 h   and solve for h = 12

Now you know the diameter of the sphere = 12    and the radius of the sphere = 6

sub this in to the volume of a sphere = 4/3  pi  r^3       and you will have your answer !

Mar 24, 2020
#2
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A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar. The volume of the cylinder is 432pi. What is the volume of the sphere?

Hello Guest!

$$432\pi =\pi r^2\cdot 2r\\ \frac{216}{\pi}=r^3$$

Not correct! I correct below.

$$V=\frac{4}{3}\cdot \pi\cdot r^3=\frac{4}{3}\cdot \pi \cdot \frac{216}{\pi}\\$$

$$V=288$$ !

Mar 24, 2020
edited by asinus  Mar 24, 2020
edited by asinus  Mar 24, 2020
#3
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I correct.

$$432\pi =\pi r^2\cdot 2r\\ \frac{432}{2}=r^3\\ \color{blue}r^3=216$$

$$V=\frac{4}{3}\cdot \pi\cdot r^3=\frac{4}{3}\cdot \pi \cdot 216\\$$

$$V=288\pi$$ !

asinus  Mar 24, 2020