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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: