Question

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

Answer 1

Answer:

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

Answer 2

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:

$V=\pi r^2h$

$64=\pi r^2h$

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:

$64=\pi r^2h$

$64=\pi r^2*2r=2\pi r^3$

$\pi r^3=64/2=32$

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:

$V=\frac{4}{3} \pi r^3$

$V=\frac{4}{3} *32=128/3$

Thus, the answer is C.