The surface area of a cylinder is 200cm. The diameter is equal to the height. Find the radius.
V= πr^2h, but h = r
so V=πr^3 = 200
r^3 = 200/π
r = appr. 4 cm .......(I had 3.9929)
Forget this
I read it as volume
Time to go to bed.
SA = 2πr^2 + 2πrh , but h=r
= 2πr^2 + 2πr^2 = 4πr^2
4πr^2 = 200
r^2 = 200/4π
r = 3.989 or appr. 4
Well, what do you know, the answers were the same.
FYI
Reiny, I didn't see that you had already solved this problem before I answered the same same post below.
I noticed are answers were different.
The height = diameter, not radius.
I am not sure if 'Scratch my reply" means your 1st answer here or your 2nd answer.
To find the radius of the cylinder, we first need to understand the formula for calculating the surface area of a cylinder.
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh
Given that the diameter is equal to the height, we can infer that the height (h) is also equal to twice the radius (r).
Therefore, we can rewrite the formula as:
Surface Area = 2πr² + 2πr(2r)
Surface Area = 2πr² + 4πr²
Surface Area = 6πr²
Now, we can substitute the given surface area (200cm) into the formula and solve for the radius (r):
200 = 6πr²
To find the radius, we can rearrange the equation as follows:
r² = 200 / (6π)
r² = 100 / (3π)
Now we can solve for r by finding the square root of both sides of the equation:
r = √(100 / (3π))
Using a calculator, we can evaluate this expression:
r ≈ 4.19 cm
Therefore, the radius of the cylinder is approximately 4.19 cm.