A cylinder has a volume of 239 cubic centimetres and a height of 6 centimeters. what is the Height?
We are given that the volume of the cylinder is 239 cubic centimetres and its height is 6 centimeters.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
We can rearrange this formula to solve for h: h = V / (πr^2).
However, we are not given the radius of the cylinder, so we need to find it first.
The formula for the volume can also be written as V = Bh, where B is the base area of the cylinder (which is the area of the circle with radius r).
We can rearrange this formula to solve for the radius: r = √(V / πh).
Plugging in the given values, we get:
r = √(239 / (π * 6)) ≈ 2.31 centimeters.
Now we can use the formula for h:
h = V / (πr^2) = 6.0 centimeters (to one decimal place).
Therefore, the height of the cylinder is 6.0 centimeters.
To find the height of the cylinder, we need to 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, π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height.
In this case, we are given that the volume V is 239 cubic centimeters and the height h is 6 centimeters.
Substituting the given values into the formula, we have:
239 = π * r^2 * 6
To find the height h, we need to solve for r first.
Dividing both sides of the equation by (π * 6) gives:
239 / (π * 6) = r^2
Simplifying the equation, we have:
r^2 ≈ 12.76595744
Taking the square root, we get:
r ≈ √12.76595744
r ≈ 3.57
So, the radius of the cylinder is approximately 3.57 centimeters.
Now, let's solve for h.
Substituting the radius r and the volume V into the formula, we have:
239 = π * 3.57^2 * h
Simplifying the equation:
239 = 3.14 * 12.7449 * h
239 = 40.085386 * h
Dividing both sides of the equation by 40.085386, we get:
h ≈ 5.97
Therefore, the height of the cylinder is approximately 5.97 centimeters.