The volume of a cylinder is 980 in.. The height of the cylinder is 20 in. What is the radius of the cylinder?
Express your answer to the nearest hundredth.
V=πr2h
Solve for r.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder. The formula is:
V = π * r^2 * h
where V is the volume, π is approximately 3.14, r is the radius, and h is the height.
In this case, the volume of the cylinder is given as 980 in^3, and the height is given as 20 in. We need to solve for the radius, so let's rearrange the formula to isolate the radius.
Start with the formula: V = π * r^2 * h.
Divide both sides of the equation by (π * h) to isolate r:
V / (π * h) = r^2.
Now let's substitute the given values into the formula:
980 in^3 / (3.14 * 20 in) = r^2.
Simplify the expression:
49.267 in^2 ≈ r^2.
To find r, we take the square root of both sides of the equation:
√(49.267 in^2) ≈ √(r^2).
r ≈ 7 in.
Therefore, the radius of the cylinder is approximately 7 inches.
To find the radius of a cylinder, we can use the formula for the volume of a cylinder:
V = π * r^2 * h
Where:
V = Volume
π = Pi (approximately 3.14)
r = radius
h = height
Given:
V = 980 in^3
h = 20 in
Let's rearrange the formula to solve for the radius (r):
r^2 = V / (π * h)
Substituting the given values:
r^2 = 980 / (3.14 * 20)
r^2 ≈ 15.59
Taking the square root of both sides:
r ≈ √15.59
r ≈ 3.95
Therefore, the radius of the cylinder is approximately 3.95 inches when rounded to the nearest hundredth.