The volume of a hemisphere is 250pi/3. Inches cubed. What is the radius
To find the radius of a hemisphere when given its volume, you can use the formula for the volume of a hemisphere:
V = (2/3) * π * r^3
Here, "V" represents the volume and "r" represents the radius.
In this case, we are given that the volume (V) of the hemisphere is 250π/3 cubic inches. Therefore, we can set up the equation as follows:
250π/3 = (2/3) * π * r^3
To solve for "r," we can isolate the radius term:
250π/3 = (2/3) * π * r^3
Dividing both sides by (2/3) * π yields:
(250π/3) / ((2/3) * π) = r^3
Simplifying the expression on the left side gives:
(250π/3) ÷ (2/3) = r^3
Canceling out the common terms on the left side will result in:
250π ÷ 2 = r^3
Simplifying the expression further:
125π = r^3
Finally, to find the radius (r), we take the cube root of both sides of the equation:
r = ∛(125π)
Calculating the cube root of 125 will give us:
r ≈ ∛(125) ≈ 5
Thus, the radius of the hemisphere is approximately 5 inches.