A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of 320pi cubic feet. What is the diameter, in feet, of the water tank?
V = π r^2 h
320π = π(r^2)(20)
r^2 = 320π/(20π) = 16
r = 4
so the diameter is 8
Thx helped me on test
To find the diameter of the water tank, we need to use the formula for the volume of a cylinder. The formula for the volume of a cylinder is given by:
Volume = π * r^2 * h
where:
- π is the mathematical constant equal to approximately 3.14159,
- r is the radius of the cylinder, and
- h is the height of the cylinder.
In this case, we are given the height of the cylinder as 20 feet and the volume as 320π cubic feet. Substituting these values into the formula, we can solve for the radius.
320π = π * r^2 * 20
Dividing both sides of the equation by π * 20:
(320π) / (π * 20) = r^2
Simplifying:
320 / 20 = r^2
16 = r^2
Taking the square root of both sides:
r = √16
r = 4
The radius of the cylinder is 4 feet. Since the diameter of a circle is twice the radius, the diameter of the cylinder is:
diameter = 2 * radius = 2 * 4 = 8 feet
Therefore, the diameter of the water tank is 8 feet.
To find the diameter of the water tank, we can use the formula for the volume of a right circular cylinder:
V = πr^2h,
where V is the volume, r is the radius of the base, and h is the height.
In this case, the volume of the water tank is given as 320π cubic feet, and the height is given as 20 feet. Let's plug in the values we know into the formula:
320π = πr^2 * 20.
Simplifying the equation, we divide both sides by 20π:
16 = r^2.
Taking the square root of both sides, we find:
r = 4.
Now, we have the radius of the base (r), and we need to find the diameter (d). The diameter is twice the radius, so we can calculate it as:
d = 2r = 2 * 4 = 8.
Therefore, the diameter of the water tank is 8 feet.