what would have a greater surface area? a cylinder that is flat and smooth or a cylinder that is threaded? I think the smooth one will because the threads remove area that needs to be covered?
no, the threads replace a smooth area with two sides of a groove. Two sides of a triangle add up to more than the third side.
To determine which cylinder would have a greater surface area, let's break down the calculation and compare the two scenarios.
A cylinder consists of two circular bases and a curved lateral surface. The formula for the surface area of a cylinder is:
Surface Area = 2πr^2 + 2πrh
Where:
- r is the radius of the circular base
- h is the height of the cylinder
Assuming the height (h) and radius (r) are the same for both cylinders, we can focus on the differentiating factor: the threaded surface of one cylinder.
In the case of a smooth cylinder, the entire lateral surface is flat and contributes to the surface area calculation. So the surface area is evenly distributed around the curved surface.
Conversely, for a threaded cylinder, a portion of the lateral surface is replaced by threads. The threads remove some of the curved area, resulting in a decreased surface area compared to the smooth cylinder. Therefore, your intuition is correct.
To find the exact surface area difference, we would need the dimensions of the threads (depth, pitch, etc.) and their number per unit length. With this information, we could calculate the total decrease in surface area caused by the threads. However, without these specifics, it is safe to assume that the smooth cylinder will have a greater surface area than the threaded cylinder.