Question

The distance around the middle of a sphere (the circumference) equals 25.1327 in. What is the volume of the sphere?

a) 107.32 in³
b) 134.15 in³
c) 179.85 in³
d) 214.72 in³

Answer 1

The volume of the sphere is approximately 107.32 in³.

Step-by-step explanation:

The volume of a sphere is calculated using the formula:

V = (4/3)πr³

Given that the distance around the middle of the sphere (circumference) is 25.1327 in., we can use the formula to find the radius, and then calculate the volume.

To find the radius, we can use the formula:

C = 2πr

Substituting the given circumference value, we have:

25.1327 = 2πr

Dividing both sides by 2π, we get:

r = 25.1327 / (2π)

Now, we can substitute the value of the radius into the volume formula:

V = (4/3)π(25.1327 / (2π))³

Simplifying further:

V = (4/3)π(6.366/π)³

V ≈ 107.32 in³