Question

The diameter of a sphere is 8 centimeters. What is the volume of the sphere? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. cm³

Answer 1

the steps for this are below

recall volume of sphere formula is

`(4)/(3) \pi * r {}^(3)`
we know the diameter so to get the radius we just divide the diameter by 2 to get the radius

`r = 8 / 2`

`r = 4`
know we can plug it into the volume of a sphere formula and solve using 3.14 for pi

`v = (4 * 3.14 * 4 {}^(3) ) / 3`
simplify the parentheses and get

`v = (803.84)/(3)`
FINAL ANSWER (rounding to nearest tenth)

`v = 267.9 \: cm {}^(3)`

Answer 2

The volume of a sphere is given by the equation
`V= (4)/(3) \pi r^3`, where r is the radius.

We are given the diameter of the sphere, but recall that the diameter is twice the radius:
`d=2r`. So the radius is half of the diameter:
`r= (1)/(2)d`.

Half of 8 cm is 4 cm.

We substitute this for r in the equation and we use 3.14 for π.


`V= (4)/(3)(3.14)(4)^3= ((4^4)(3.14))/(3)=267.9 \ cm^3`