The volume of a sphere with radius r can be written as the function V (r) = 4/3πr^3
Determine the inverse of this function and use it to find the radius of a sphere with a volume of 50 cm^3 Round to two decimal places.
To find the inverse of the function V(r) = 4/3πr^3, we need to switch the roles of r and V and solve for r:
V = 4/3πr^3
V/(4/3π) = r^3
3V/(4π) = r^3
r = (3V/(4π))^(1/3)
Now, we have the inverse function:
r = (3V/(4π))^(1/3)
Given that V = 50 cm^3, we can plug in this value to find the radius:
r = (3(50)/(4π))^(1/3)
r = (150/(4π))^(1/3)
r = 7.67 cm
Therefore, the radius of a sphere with a volume of 50 cm^3 is approximately 7.67 cm.