What is the radius of a cylinder with a volume of 432pi cm^3 if the height of the cylinders is equal to its diameter?
pi R^2 * (2R) = 432 pi
2 R^3 = 432
R^3 = 216
R = 6 cm
Thank you so much
To find the radius of a cylinder with a volume of 432π cm^3 and a height equal to its diameter, we can follow these steps:
Step 1: Recall the formula for the volume of a cylinder:
V = π * r^2 * h
Step 2: Since the height is equal to the diameter, h = 2r.
So, the volume formula can be rewritten as:
V = π * r^2 * (2r)
Step 3: Substitute the given volume into the equation:
432π = π * r^2 * (2r)
Step 4: Simplify the equation:
432π = 2π * r^3
Step 5: Divide both sides of the equation by 2π:
216 = r^3
Step 6: Take the cube root of both sides of the equation:
r = ∛216
Step 7: Simplify the cube root of 216:
r = 6
Therefore, the radius of the cylinder is 6 cm.
To find the radius of a cylinder with a given volume, we first need to understand the formula for the volume of a cylinder. The formula for the volume of a cylinder is:
V = πr^2h
where V represents the volume, r represents the radius, and h represents the height of the cylinder.
In this case, the volume is given as 432π cm^3, and the height (h) is equal to the diameter (which is twice the radius). Let's denote the radius as r. Therefore, the height h would be 2r.
Substituting these values into the formula, we get:
432π = πr^2(2r)
Simplifying the equation, we can divide both sides by π:
432 = 2r^3
Now, divide both sides by 2:
216 = r^3
To find the radius (r), we need to take the cube root of both sides:
r = ∛216
Calculating the cube root of 216, we find that the radius (r) is 6 cm.
Therefore, the radius of the cylinder is 6 cm.