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?
+36916 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 !
+14917 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.
\(V=\frac{4}{3}\cdot \pi\cdot r^3=\frac{4}{3}\cdot \pi \cdot \frac{216}{\pi}\\ \)
\(V=288\)
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