A cylinder has a surface area of 250cm2. The height is twice as big as the radius. What is the height of the cylinder?
h = 2r
SA = 2πr^2 + 2πrh
= 2πr^2 + 2πr(2r)
= 6πr^2
6πr^2 = 250
r^2 = 125/(3π)
r = 3.6418..
h = 2r = 7.28....
To find the height of the cylinder, we need to use the formula for the surface area of a cylinder:
Surface Area = 2πr(r + h)
where r is the radius and h is the height.
In this case, we know that the surface area is 250 cm^2. Therefore, we can write the equation as:
250 = 2πr(r + h)
Since the height (h) is given as twice the radius (r), we can substitute it into the equation:
250 = 2πr(r + 2r)
Now, we simplify the equation:
250 = 2πr(3r)
250 = 6πr^2
Next, we divide both sides of the equation by 6π to isolate the r^2 term:
250 / (6π) = r^2
Finally, we take the square root of both sides to find the value of r:
r = √(250 / (6π))
r ≈ 3.18 cm
Now that we have the value of r, we can find the height (h), which is twice the radius:
h = 2r
h = 2 * 3.18 cm
h ≈ 6.36 cm
Therefore, the height of the cylinder is approximately 6.36 cm.