Question

What is the approximate volume of the sphere if the surface area is 482.8 mm²?

Answer 1

To find the volume of a sphere, we can use the formula:

V = (4/3)πr^3

Given that the surface area is 482.8 mm², we can find the radius using the formula:

A = 4πr^2

Rearranging the equation, we get:

r^2 = A / (4π)
r^2 = 482.8 / (4π)
r^2 ≈ 38.48

Taking the square root of both sides, we find:

r ≈ √38.48
r ≈ 6.21 mm

Now we can substitute the value of 'r' into the volume formula:

V ≈ (4/3)π(6.21)^3
V ≈ 524.81 mm³

Therefore, the approximate volume of the sphere is 524.81 mm³.

Answer 2

that is not correct

Answer 3

Apologies for the incorrect response. Let's calculate the approximate volume of the sphere correctly.

Given that the surface area is 482.8 mm², we can find the radius using the formula:

A = 4πr²

Rearranging the equation, we have:

r² = A / (4π)
r² = 482.8 / (4π)
r² ≈ 38.48

Taking the square root of both sides, we find:

r ≈ √38.48
r ≈ 6.21 mm

Now, let's calculate the volume using the updated radius:

V = (4/3)πr³
V ≈ (4/3)π(6.21)³
V ≈ (4/3)π(6.21)(6.21)(6.21)
V ≈ (4/3)π(149.22)
V ≈ 198.74π

Using an approximation of π as 3.14, we can calculate the approximate volume:

V ≈ 198.74 * 3.14
V ≈ 624.67 mm³

Therefore, the approximate volume of the sphere is 624.67 mm³.