V = (3.14)(r)^2(h/3) = 50 cm^3
what is the radius and height
To solve for the radius and height, we can rearrange the formula for the volume and substitute the given value.
Let's start by rewriting the formula:
V = π * r^2 * (h/3) = 50 cm^3
Now we can substitute V with 50 cm^3:
50 = π * r^2 * (h/3)
As the volume is given as 50 cm^3, we can simplify the equation further:
50 = (π/3) * r^2 * h
To isolate r^2 * h, we divide both sides of the equation by (π/3):
50 / (π/3) = r^2 * h
Now, we can calculate r^2 * h:
r^2 * h = (50 * 3) / π
r^2 * h = 150 / π
Since r^2 * h is a constant, we will designate it as k for convenience:
k = 150 / π
Now we can solve for the radius and height separately.
To find the radius (r), we take the square root of k and divide it by π:
r = √(k/π) = √(150/π) ≈ 4.33 cm
To find the height (h), we substitute the value of r in the original equation and solve for h:
50 = π * (4.33)^2 * (h/3)
50 = 3.14 * 18.6949 * (h/3)
50 = 58.705686 * (h/3)
h/3 = 50 / 58.705686
h/3 ≈ 0.852 cm
To find the height (h), we multiply both sides by 3:
h ≈ 0.852 * 3 ≈ 2.557 cm
Therefore, the radius (r) is approximately 4.33 cm and the height (h) is approximately 2.557 cm.