Normally, I'm not bad with my math formulas but, in my current lesson I have having some issues. Can somebody please provide me with a (non-complicated) formula for finding the surface area and lateral are for both cylinders and prisms? Any help is much appreciated! Thanks
cylinders are easy:
Consider a can of height h, and radius r
Visualize taking off both lids of a tin can, you would have 2 circles.
Now cut the "sleeve" along the height then fold it flat, and you would have a rectangle of length 2πr and height h
So the surface area
= 2πr^2 + 2πrh or 2πr(r + h)
Prism is much too vague of a term, since there are so many different kinds of prism
https://www.google.ca/search?q=prisms&rlz=1C5CHFA_enCA690CA690&espv=2&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwjakZ6VqZLTAhUo2IMKHSl8DXsQsAQIIA&biw=1668&bih=926
Now, if you Google something like
"surface area of triangular prism" you will get an overwhelming amount of information.
Just become selective.
It helps if you can visualize your shape separated into flat surfaces, called a net, then finding the areas of the different shapes.
Of course! I can help you with that. Let's start with the formulas for finding the surface area and lateral area of cylinders and prisms.
1. Surface area of a cylinder:
The surface area of a cylinder consists of two bases and the curved surface area. The formula is:
Surface Area = 2πr^2 + 2πrh,
where "r" represents the radius of the cylinder's base and "h" represents the height of the cylinder.
2. Lateral area of a cylinder:
The lateral area of a cylinder refers to only the curved surface area. The formula is:
Lateral Area = 2πrh.
3. Surface area of a prism:
The surface area of a prism is the sum of the areas of all its faces. The formula depends on the shape of the base(s). For example, if the base is a rectangle, the formula is:
Surface Area = 2lw + 2lh + 2wh,
where "l" represents the length, "w" represents the width, and "h" represents the height of the prism.
4. Lateral area of a prism:
The lateral area of a prism consists of the areas of all the lateral faces. Again, the formula depends on the shape of the base(s). For a prism with a rectangular base, the formula is simply:
Lateral Area = 2lh + 2wh.
In summary, for cylinders, you have separate formulas for surface area and lateral area, while for prisms, the surface area and lateral area formulas are the same. Just remember to correctly identify the dimensions (such as radius, height, length, width) when plugging them into these formulas.
I hope that helps! If you have any further questions, feel free to ask.