The volume of a cylinder with a height of 14 cm is 503 cm^3 503 c m 3. Find the radius of the base of the cylinder. Round to the nearest hundredth
π * r^2 * 14 = 503
r = √[503 / (14 * π)]
To find the radius of the base of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given that the height (h) is 14 cm and the volume (V) is 503 cm^3, we have:
503 = π * radius^2 * 14
To solve for the radius (r), we can rearrange the equation:
radius^2 = 503 / (π * 14)
radius^2 ≈ 503 / 43.98
radius^2 ≈ 11.437
To find the radius, we take the square root of both sides:
radius ≈ √11.437
radius ≈ 3.38
Rounding to the nearest hundredth, the radius of the base of the cylinder is approximately 3.38 cm.
To find the radius of the base of the cylinder, we can use the formula for the volume of a cylinder.
The formula for the volume of a cylinder is:
V = π * r^2 * h
where V is the volume, r is the radius, and h is the height.
Given that the volume of the cylinder is 503 cm^3 and the height is 14 cm, we can rearrange the formula to solve for the radius:
503 = π * r^2 * 14
Now we can isolate the radius by dividing both sides of the equation by (π * 14):
503 / (π * 14) = r^2
To find the value of r, we need to divide 503 by (π * 14):
r^2 = 503 / (π * 14)
Now, take the square root of both sides to solve for r:
r = √(503 / (π * 14))
Using a calculator and substituting the value of π as approximately 3.14, we can evaluate this expression to find the value of r:
r ≈ √(503 / (3.14 * 14))
r ≈ √(11.407)
r ≈ 3.38 (rounded to the nearest hundredth)
Therefore, the radius of the base of the cylinder is approximately 3.38 cm (rounded to the nearest hundredth).