This cylinder has a volume of 12 pi cubic inches and a diameter of 4 inches. Find the cylinder's radius and height.
To find the radius and height of the cylinder, we can use the formulas and equations related to the volume and diameter of a cylinder.
First, let's recall the formula for the volume of a cylinder:
Volume of a cylinder = π * r^2 * h
where π is a constant value approximately equal to 3.14159, r is the radius of the cylinder, and h is the height of the cylinder.
We are given the volume of the cylinder as 12π cubic inches. Substituting this value into the equation, we have:
12π = π * r^2 * h
Since π is a common factor on both sides of the equation, we can cancel it out:
12 = r^2 * h
Now let's consider the information about the cylinder's diameter. The diameter is given as 4 inches, and we know that the radius is half the diameter. Therefore, the radius (r) is 4/2 = 2 inches.
Substituting this value into the equation, we have:
12 = (2)^2 * h
12 = 4 * h
Next, we can solve for the height (h) by dividing both sides of the equation by 4:
h = 12/4
h = 3 inches
Therefore, the radius of the cylinder is 2 inches and the height is 3 inches.
if the diameter is 4, then the radius is 2, right?
you know that
v = πr^2 h, so
4πh = 12π
so h = 3 ft