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.
V = (3.14)(r)^2(h/3) = 50 cm^3
what is the radius and height
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1 answer