A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed. A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 12 centimeters cubed 24 centimeters cubed 36 centimeters cubed 54 centimeters cubed

12 cm³

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.