To find the value of x in the equation for the volume of a sphere, we need to recall the formula for the volume of a sphere, which is given by:
V = rac{4}{3}πr³
In this formula, V represents the volume of the sphere, and r is the radius. From the question, we know that the volume V is equal to 5003π cubic units.
Setting the equation, we have:
5003π = rac{4}{3}πr³
We can divide both sides by π to simplify the equation:
5003 = rac{4}{3}r³
Next, we can eliminate the fraction by multiplying both sides by 3:
15009 = 4r³
Now, we divide both sides by 4:
r³ = rac{15009}{4}
Calculating that gives us:
r³ = 3752.25
To find the value of r, we take the cube root of 3752.25:
r =
oot{3}{3752.25} ≈ 15.43
Assuming that x refers to the radius of the sphere, we conclude:
x ≈ 15.43
This means that the radius of the sphere is approximately 15.43 units.