Answer:
C. 128/3 meters cubed
Step-by-step explanation:
The volume of a cylinder is denoted by: [tex]V=\pi r^2h[/tex], 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:
[tex]V=\pi r^2h[/tex]
[tex]64=\pi r^2h[/tex]
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:
[tex]64=\pi r^2h[/tex]
[tex]64=\pi r^2*2r=2\pi r^3[/tex]
[tex]\pi r^3=64/2=32[/tex]
Now, the volume of a sphere is denoted by: [tex]V=\frac{4}{3} \pi r^3[/tex], where r is the radius. From above, we know that [tex]\pi r^3=32[/tex], so we can plug this into the equation:
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} *32=128/3[/tex]
Thus, the answer is C.
