The volume of a sphere is equal to its surface area. What is the diameter of the sphere?
area of a sphere=4(pi)r^2
volume=(4/3)(pi)r^3
now equate them and solve for r
then
diameter=twice of r
4(π)r^2=(4/3)(π)r^3
To find the diameter of the sphere, we need to use the formulas for its volume and surface area. Let's consider the formulas:
The volume of a sphere is given by V = (4/3) * π * r^3, where r represents the radius of the sphere.
The surface area of a sphere is given by A = 4 * π * r^2.
We are given that the volume of the sphere is equal to its surface area, so we can set up the equation:
V = A
By substituting the formulas for volume and surface area, we get:
(4/3) * π * r^3 = 4 * π * r^2
We can now solve for r:
(4/3) * π * r^3 = 4 * π * r^2
Divide both sides by (4/3) * π (pi):
r^3 = (4 * π * r^2) / ((4/3) * π)
Cancel out the common terms:
r^3 = r^2 / (1/3)
Multiply both sides by (1/3):
r^3 * (1/3) = r^2
Simplify:
r^3 = (1/3) * r^2
Divide both sides by r^2:
r = 1/3
Now that we know the radius of the sphere is 1/3, we can find the diameter by doubling the radius:
d = 2 * r
Substituting the value of the radius:
d = 2 * (1/3) = 2/3
Therefore, the diameter of the sphere is 2/3 units.