Surface Area and volume: Surface Area and volume Archit Gupta IX-A 7
Slide 2: Surface area of cube Surface area of cuboid Total surface area of cylinder Surface area of sphere Total surface area of cone Total Surface area of hemisphere Curved surface area of cylinder Curved surface area of cone Curved surface area of hemisphere Volume of cube Volume of cuboid Volume of cylinder Volume of cone Volume of sphere Volume of hemisphere
Surface area of cuboid: Surface area of cuboid A cuboid is made up of (6) rectangular faces. Area of – Rectangle 1-LxH Rectangle 2-LxB Rectangle 3-LxH Rectangle 4-LxB Rectangle 5-BxH Rectangle 6-BxH Surface area of cuboid=2(lb+bh+hl)
Surface area of cube: Surface area of cube A cube has six (6) faces and each face is in shape of square. If the area of each square is a 2 then 6 faces is 6a 2 Surface area of cube=6a 2
Curved surface area of cylinder: Curved surface area of cylinder Curved surface area of an object is the area of outer covering of it. If a rectangular paper is folded ,the length becomes the circumference and the breadth becomes the height. So csa of a cylinder is 2 π r x height . Curved surface area of cylinder=2 π rh
Total surface area of cylinder : Total surface area of cylinder Total surface area of an object is the area of whole body. If a rectangular paper is folded ,the length becomes the circumference and the breadth becomes the height. So tsa of a cylinder is 2 π rh+2 π r 2 =2 π r(r+h). Total surface area of cylinder=2 π r( r+h )
Curved surface area of cone: Curved surface area of cone If a circular paper is taken and a triangle is cut out of it the curved plane is taken as the base and diagonal to be length then triangles are formed and after taking the area of each triangle is taken then csa of cone is ½ x l x 2 π r= π rl Curved surface area of cone= ½ x l x 2 π r= π rl
Total surface area of cone : Total surface area of cone In the figure the tilted base can be taken as length(l),the straight line can be height(h) and radius can be (r). Then l 2 =r 2 +h 2 by Pythagoras Theorem. Therefore l = √ r 2 +h 2 . So- Total surface area of cone= π rl + π r 2 = π r(l + r)
Surface area of sphere: Surface area of sphere A sphere is a round shape. If we wrap a string around a sphere and draw four circles on a paper of the same radius as of the sphere and try to wrap the string around the four circles they fit so we get to know that Surface area of sphere is 4 π r 2 . surface area of sphere= 4 π r 2
Curved surface area of hemisphere: Curved surface area of hemisphere A hemisphere is the half of a sphere and as we know that the area of sphere is 4 π r 2 .So Curved surface area of hemisphere is half of that of sphere = 2 π r 2 . Curved surface area of hemisphere = 2 π r 2 .
Total Surface area of hemisphere: Total Surface area of hemisphere The Total Surface area of hemisphere can be defined as the sum of Curved surface area of hemisphere + the area of plane= 2 π r 2 + π r 2 = 3 π r 2 . Total Surface area of hemisphere=2 π r 2 + π r 2 = 3 π r 2 .
Volume of cube: Volume of cube A cube is a solid shape with four edges of equal length. So the volume is l x b x h =edge x edge x edge =a 3 Volume of cube= l x b x h =edge x edge x edge =a 3
Volume of cuboid: Volume of cuboid A cuboid is a solid shape with four edges with two pairs of sides with equal length. So the volume is base area x height= l x b x h. Volume of cuboid =base area x height= length x breadth x height=l x b x h
Volume of cylinder: Volume of cylinder The volume of a cylinder can be described as base area x height= π r 2 x height = π r 2 h. Volume of cylinder = π r 2 h.
Volume of cone: Volume of cone A cone is in shape of cylinder but as we go further we proceed towards its tip. So if we take a cylinder and a cone of same radii then fill the cone with sand or any liquid then we can only fill the cylinder after three times filling the cone. So we get to know that volume of cone is 1/3 π r 3 . volume of cone=1/3 π r 3 .
Volume of sphere: Volume of sphere To measure the volume of sphere we have to take three spheres of different radii. We put them in a cylindrical container(full of water) time to time and then measure the amount of water that fell out of the container and evaluate it by 4/3 π . Then we find that the volume of sphere is 4/3 π r 3 . surface area of sphere= 4 π r 2
Volume of hemisphere: Volume of hemisphere As we know that the volume of sphere is 4/3 π r 3 and hemisphere is half of sphere. So volume of hemisphere is half of that of sphere i.e. 2/3 π r 3 volume of hemisphere =2/3 π r 3
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