Answer:
C. 128/3 meters cubed
Step-by-step explanation:
The volume of a cylinder is denoted by: V=\pi r^2h, where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:
V=\pi r^2 h
64=\pi r^2 h
We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with
2r:64=\pi r^2 h
64=\pi r^2*2 r=2\pi r^3
\pi r^3=64/2=32
Now, the volume of a sphere is denoted by: V=\frac{4}{3} \pi r^3, where r is the radius. From above, we know that \pi r^3=32, so we can plug this into the equation:
V=\frack{4}{3} \pi r^3
V=\frack{4}{3} *32=128/3
Thus, the answer is C.
