Question

1.What is the approximate diameter of a sphere with a volume of 128π cubic inches?

Answer 1

diameter =
`8√(6)` inches

Explanation:

The formula for the volume of a sphere:

`V = (4)/(3) \pi r^(2)`

Plug in known variable, V

`128\pi = (4)/(3) \pi r^(2)`

divide by pi

`128 = (4)/(3)r^2`

divide by 4/3

`96 = r^2`

take the square root to isolate r

`r = √(96)`

`r = √(4 * 4 * 6)`

r =
`4√(6)`

double r for diameter

`4√(6) * 2 = 8\sqrt6`

Answer 2

Answer:

8.62 inches.

Step by step solved:

We are given that the volume of the sphere is 128π cubic inches. We can use this information to solve for the radius of the sphere as follows:

V = (4/3)πr^3
128π = (4/3)πr^3
r^3 = (128π)/(4/3)π
r^3 = 96
r = ∛96
r ≈ 4.31 inches (rounded to two decimal places)

The diameter of the sphere is twice the radius, so the approximate diameter of the sphere is:

d ≈ 2r
d ≈ 2(4.31)
d ≈ 8.62 inches (rounded to two decimal places)

Therefore, the approximate diameter of the sphere with a volume of 128π cubic inches is 8.62 inches.