1.What is the diameter of a sphere that has a volume of 3052.08 m^3?
My answer is: 9m
2.What is the radius of a sphere that has a volume of 2304π m^3?
My answer is:12m
~If i get it wrong please explain it to me how to get it, i know the formula and how to solve it with points but i dont know how to solve for a point, formula:V=4/3(3.14)r^3
To solve for the diameter of a sphere with a given volume, we need to use the formula for the volume of a sphere, which is V = (4/3)πr^3. In this formula, V represents the volume and r represents the radius of the sphere.
For the first question, the volume is given as 3052.08 m^3. We need to solve for the radius first and then use that value to find the diameter. Let's set up the equation:
3052.08 = (4/3)πr^3
To solve for r, we can start by dividing both sides of the equation by (4/3)π:
(4/3)πr^3 = 3052.08
r^3 = (3052.08 * 3) / (4π)
r^3 = 9156.24 / (4π)
r^3 ≈ 729
Now, we can find the cube root of both sides to solve for r:
r ≈ ∛729
r ≈ 9
The radius of the sphere is approximately 9 meters. To find the diameter, we simply double the radius:
d = 2r
d ≈ 2 * 9
d ≈ 18
So, the diameter of the sphere with a volume of 3052.08 m^3 is approximately 18 meters.
For the second question, the volume is given as 2304π m^3. Similar to the previous question, let's set up the equation:
2304π = (4/3)πr^3
To solve for r, we can divide both sides of the equation by (4/3)π:
(4/3)πr^3 = 2304π
r^3 = (2304π * 3) / (4π)
r^3 = 576 * 3
r^3 = 1728
Now, find the cube root of both sides:
r ≈ ∛1728
r ≈ 12
The radius of the sphere is approximately 12 meters.
Remember, to find the diameter, you simply double the radius. So the diameter is given by:
d = 2r
d ≈ 2 * 12
d ≈ 24
Therefore, the diameter of the sphere with a volume of 2304π m^3 is approximately 24 meters.