The volume of a sphere is 7776 pi mm3. Find the radius of the sphere
To find the radius of the sphere, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that the volume of the sphere is 7776π mm^3, we can set up the equation:
7776π = (4/3) * π * r^3
Now, let's simplify the equation by canceling out the π:
7776 = (4/3) * r^3
To isolate the radius, let's multiply both sides of the equation by (3/4):
7776 * (3/4) = r^3
5844 = r^3
Take the cube root of both sides to solve for r:
∛5844 = ∛r^3
∛5844 ≈ 17.92
Therefore, the approximate radius of the sphere is 17.92 mm.
To find the radius of a sphere when given its volume, you'll need to use the formula for the volume of a sphere. The formula is:
V = (4/3) * π * r^3
Where:
V = volume of the sphere
π = Pi (approximately 3.14159)
r = radius of the sphere
In this case, we know that the volume of the sphere is 7776π mm^3. So, we can substitute this value into the formula and solve for the radius (r).
7776π = (4/3) * π * r^3
To simplify the equation, we can cancel out the common π terms on both sides:
7776 = (4/3) * r^3
Now, let's isolate r^3 by multiplying both sides by (3/4):
7776 * (3/4) = r^3
To compute this, multiply 7776 by 3/4:
5832 = r^3
Finally, to find the radius, we need to find the cube root of 5832:
r = ∛5832
Using a calculator or computing software, the cube root of 5832 is 18. Therefore, the radius of the sphere is 18 mm.
V = (4/3)π r^3
(4/3)π r^3 = 7776π
(4/3)r^3 = 7776
r^3 =5832
take the cube root of 5832