A cylinder has a surface area of 250cm2

. The height is twice as big as the radius. What is the
height of the cylinder?

V = πr^2 h, but h = 2r

so
V = πr^2 (2r)
= 2πr^3

then 2πr^3 = 250
r^3 = 125/π
r = cuberoot(125/π)
h = 2r = 2 cuberoot(125/π) = appr 6.83 cm

To find the height of the cylinder, we can use the formula for the surface area of a cylinder:

Surface Area = 2πrh + 2πr^2

Given that the surface area of the cylinder is 250 cm^2, we can set up the equation:

250 = 2πrh + 2πr^2

Since the height (h) is twice as big as the radius (r), we can substitute h = 2r:

250 = 2πr(2r) + 2πr^2

Simplifying the equation:

250 = 4πr^2 + 2πr^2

250 = 6πr^2

Now we can solve for r by dividing both sides of the equation by 6π:

250 / (6π) = r^2

To find the value of r, follow these steps:

1. Divide 250 by 6.
2. Divide the result by π.
3. Take the square root of the value obtained in step 2.

Once you have the value of r, you can find the height (h) since it is twice the radius (h = 2r).