The volume of a sphere is 3,052.08 units cubed. What is its diameter?
4/3 * pi*r^3 = 3052.08.
4/3 * 3.14*r^3 = 3052.08,
4.19r^3 = 3052.08,
r^3 = 728.63,
r = 9,.
Dia. = 2 * 9 = 18
I get 18
Why did the sphere start singing out of nowhere? Because it wanted to "measure up" to all the other shapes! Now, let's get down to business and calculate that diameter for you.
The formula for the volume of a sphere is V = (4/3) * π * r³, where V is the volume and r is the radius. Since we have the volume, we can rearrange the formula to solve for the radius:
r = (∛(3V)/(4π))
Given that the volume is 3,052.08 units cubed, we can substitute it into the formula:
r = (∛(3 * 3,052.08)/(4 * π))
r ≈ (∛(9,156.24)/(4 * π))
r ≈ (∛2,392.08)
r ≈ 13.40 units
Now that we've found the radius, we can double it to get the diameter:
d = 2r
d ≈ 2 * 13.40
d ≈ 26.80 units
So, the diameter of the sphere is approximately 26.80 units. Keep in mind that this is just a rough estimate - circles can be downright slippery to measure!
To find the diameter of a sphere given its volume, we need to use the formula that relates the volume of a sphere to its radius or diameter.
The formula for the volume of a sphere is:
V = (4/3) * π * r^3
Here, V represents the volume of the sphere, π is a mathematical constant approximately equal to 3.14159, and r represents the radius of the sphere.
We know that the volume of the sphere is 3052.08 units cubed. So we can rewrite the formula as:
3052.08 = (4/3) * π * r^3
To find the diameter, we need to find the radius first. Rearranging the formula, we get:
r^3 = (3/4) * (3052.08 / π)
r^3 ≈ 1157.5351
Taking the cube root of both sides, we find:
r ≈ ∛1157.5351
r ≈ 10.87
Finally, to find the diameter, we can multiply the radius by 2:
d = 2 * r
d ≈ 2 * 10.87
d ≈ 21.74
Therefore, the diameter of the sphere is approximately 21.74 units.