Surface Area of Prisms and Cylinders

hi this is Mario with Mario's math tutoring coming to you with another math video to help you boost your math grade improve your understanding and hopefully make math lot less stressful so in this video what we're going to talk about is how to find the surface area of prism and of cylinder now group these together prisms and cylinders because they're very similar it's like prism is basically you have two parallel and congruent faces like this and they're separated by the height okay so for cylinder cylinder basically has two circles that are parallel and congruent through the same size and shape separated by the height and you can see here is square prism you have two squares that are separated by the height and they're the same size and shape okay so to find the surface area of prism you take two times the area of the base that's what the capital represents plus the perimeter of the base that's so the represents times the height so the way this works is if you cut this and you unfold it okay you're going to end up with big rectangle like so and you're going to have top and bottom so two squares folded those like that so if you were to fold it back up you fold these and these would wrap around and that would form the the sides or what they call the lateral area but what we can do is we can find the area of this base okay these two bases and you can see it's square it's over here this is four by four so that's going to be 16 okay for the area of the base times two because we have two of them so that's 2 times 16 plus now that what's the formula for the area of rectangle well it's length times width or base times height right but you can see here the height is 8 this base is actually the perimeter okay the perimeter of the base so this is actually 4 4 4 and 4 that gives you 16 times the height times 8 so that's going to give you 8 times 16 okay so if you simplify that all out what do we get looks like we get 32 plus 128 which is hundred and sixty units squared okay so for area it's square units because you're covering this with like little one by one by one squares like you're wrapping present with little little squares right okay now this one with the cylinder imagine if we cut this open okay it's like roll and you unroll it flip the top up flip the top down or the base here downs you're going to get two circles and rectangle so that's easy enough you find the area of the circle PI squared so this case is going to be PI times 5 squared times 2 because you have top and bottom okay now this part here can be little bit challenging okay this is rectangle right but where does this dimension here come from it comes from the circumference of the circle the circumference of the base so when you cut this and you unroll it this length is actually the circumference 2 pi okay so what we're taking is we're taking the this length 2 pi times the height to give us the area of the rectangle so length times width or base times height but this represents the circumference of the circle okay so that's 2 times pi times the radius is 5 times the height which is 10 and if we simplify this we get 25 times 2 which is 50 PI plus 50 times 2 is hundred pi so we're looking at 150 PI units squared again square units because this is just area area is two-dimensional you're covering this with little squares so hope you learn something from this video hope this made finding surface area of prisms and cylinders little bit easier subscribe to the channel check out some of my past videos and stay tuned for some future videos I'll see you in the next video