Sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.

A sphere with height h and radius r. A cylinder with height h and radius r.

What is the volume of the sphere?
StartFraction 64 Over 3 EndFraction meters cubed
32 meters cubed
StartFraction 128 Over 3 EndFraction meters cubed
64 meters cubed

C. 128/3 meters cubed

Step-by-step explanation:

The volume of a cylinder is denoted by: , 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:

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:

Now, the volume of a sphere is denoted by: , where r is the radius. From above, we know that , so we can plug this into the equation:

Thus, the answer is C.

C. StartFraction 128 Over 3

Step-by-step explanation:

Volume of cylinder:

Pi × r² × h

h = 2r

Pi × r² × 2r = 64

Pi × r³ = 32

Volume of sphere:

(4/3)pi × r³

(4/3)(32)

128/3

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: