Find the volume of a sphere with a radius of 4. Round your answer to the nearest hundredth if necessary. Find the radius of a sphere with a volume of 256/3 π. Find the volume of a sphere with a diameter of 14. Round your answer to the nearest hundredth if necessary

Let’s tackle your questions one by one.

1. Find the volume of a sphere with a radius of 4.

To find the volume ( V ) of a sphere, you can use the formula:

[

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

]

Here, the radius ( r = 4 ). So we substitute:

[

V = frac{4}{3} pi (4)^3 = frac{4}{3} pi (64) = frac{256}{3} pi

]

Now, if we calculate the numerical value:

[

frac{256}{3} approx 85.33 quad text{(using } pi approx 3.14text{)}

]

Consequently, the volume is:

[

V approx 268.08 , text{cubic units (when approximating with } pi approx 3.14text{)}.

]

2. Find the radius of a sphere with a volume of ( frac{256}{3} pi ).

Using the volume formula again:

[

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

]

Setting this equal to ( frac{256}{3} pi ) gives: