Surface Area of Composite Figures Hemisphere on top of a Cylinder

hello this is mr. Kenyan Ola and I'm going to help you find the service area of composite solid made up of hemisphere and cylinder so few things to remember first thing is surface area surface area means how many squares fit on the surface and we have two shapes that two solids that make up this composite solid which is hemisphere which is just sphere cut into half and cylinder that sits on the bottom so we have this cylinder right here so we're going to be dealing with two formulas the forth first formula is the surface area of sphere so sphere is if you guys remember service area is four PI squared because it takes four circles to completely cover sphere and cylinder is equals to plus pH for the two base areas the base perimeter and distance between the two Heights however we're not going to use these formulas exactly how they're written here because with composite figures certain things are covered up and certain things we don't need certain things squares don't aren't found on the surface so if we look at this first thing is we don't have full sphere we have hemisphere which is half of sphere so if we cut that as full sphere and half for hemisphere we're going to not use 4 PI squared but we're going to use 1/2 which is 2 PI squared so we only need 2 circles to cover up this hemisphere and then for this cylinder right here we're going to change things because so for the form of our cylinder it's two bases plus the parameter base perimeter the height two bases however when we so here's the two bases for this cylinder but when we take this here are sorry Hemisphere and put it on top see how it covers up one of the bases for this cylinder so we can't there won't be any squares on the surface on this base all the squares would be on the Hemisphere and the rest of the cylinder so we don't need this second base right here so what we're going to do with this form though is take out one of the bases because it's covered up by the hemisphere and just put one b-plus base primer and height and then we'll add those two together so let's figure out what the service area of this hemisphere is it looks like our radius is 6 so we'll plug that in so 2 pi times 6 squared 6 squared is 36 PI times 2 2 times 36 is 72 pi so now we have the surface area of just this hemisphere this top part of this composite solid now it's gets the service area for this cylinder that isn't covered up by the hemisphere so just the cylinder that's wide open to put squares on so we have the 1 base and the base of this cylinder is circle so and the area of circle is PI squared so I'm going to write PI and our radius for this base right here for this circle is the same as the radius up here which is 6 so we'll write 6 squared plus now we want to get this lateral area around the cylinder Pia's base perimeter another word for perimeter of circle is circumference you guys remember the forum for circumference it's two PI so all right two pi and the radius is 6 and is the distance between these two bases which is 4 and we'll just multiply all this out so 6 squared is 36 so 36 PI this represents again the area of just this one base that's exposed we're forgetting about the second base up here because not exposed because that's hemisphere is covering it and we'll multiply this 2 times 6 is 12 times 4 is 48 pi and now we're just going to add all three of these pods you have 72 PI's here 36 PI's in 48 PI's and let's combine those like terms let's use our calculator just to make sure 72 plus 36 plus 248 which is 156 and don't forget we're talking about PI's here so PI centimeters and it's the number of squares that fit on the surface so 156 PI centimeters squared so or if your teacher wants it in decimal go again go to mode press the mode button go to classic take it off math prints and just type in 156 pi and that would be 490 point zero 8 so those will be your two answers either 156 pi centimeter squared or 490 point something something centimeters squared hope this helps the big takeaway is that when you have composite figures you don't just take the surface area of one shape and add it to the surface area the other shape you have to figure out which part of the shape is being covered up when you combine those two figures together so we figure that this covered up one of the bases so we didn't use both bases if we just use one base there you go hope it helps have great day