Surface Areas And Volumes-Baby Sudhakaran

Slide 1: 

Surface -- FORMULAE -- Areas

Slide 2: 

Surface Areas Surface Areas Of Some Solids Surface Areas Of Some Combined Solids EXIT

Slide 3: 

CUBE CUBE Surface Area We will need to find the surface area of the top, base and sides. Area of the top and bottom is 2a 2 Area of sides ( CSA ) is 4a 2 Therefore the formula is: 6a 2 Volume V = a 3 MAIN MENU NEXT a a a a

Slide 4: 

CUBOID Cuboid Surface Area We will have to calculate the area of sides, top and base. Area of sides = ( CSA ) is 2(lh+bh) Area of top and base is 2(lb) Therefore the formula is: 2(lb+lh+bh) Volume v = lbh MAIN MENU NEXT

Slide 5: 

CONE MAIN MENU NEXT TSA = ת r(s+r)

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CYLINDER MAIN MENU NEXT CSA = 2πr 2

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SPHERE MAIN MENU NEXT

Slide 8: 

HEMISPHERE Surface Area We need to find the outer surface area and the area of the base. Outer surface area (CSA) is 2 π r^2 Area of the base is π r^2 Therefore the formula is 3 π r^2 Volume V = πr^3 MAIN MENU

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SURFACE AREA OF A COMBINATION OF SOLIDS SURFACE AREA OF -- MAIN MENU NEXT

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SURFACE AREA OF A COMBINATION OF SOLIDS MAIN MENU SURFACE AREA OF -- BACK

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A Cylinder Surmounted By A Cone l h r Surface Area of the model = CSA of cone + CSA of cylinder = πrl + 2πrh = π r ( l + 2h ) BACK NOTE: The cylinder is hollow

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A Solid Cylinder With A Conical Cavity h r l Surface Area of the model = CSA of the cylinder + CSA Of the cone + Area of the cylinder’s base = 2πrh + πrl + πr 2 = πr ( 2h + l + r ) BACK

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l r A Sphere Attatched To A Cone Surface Area of the model = CSA of hemisphere + CSA of the cone = 2πr 2 + πrl = πr ( 2r + l ) BACK

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h r R Surface area of the model = CSA of the cylinder + Surface area of the sphere – Area of the cylinder’s base = 2 πrh + 4 πr 2 – πr 2 = πr ( 2h – r ) + 4πr 2 A Round Bottom Flask BACK

Slide 15: 

H h r R A Cylinder Surmounted By Another Cylinder Surface area of the model = TSA of the the larger cylinder + TSA of the smaller cylinder – Area of the smaller cylinder’s base = 2πRH + 2πR 2 + 2πrh + 2πr 2 – πr 2 = 2πR ( H + R ) + 2πr ( h + r ) BACK

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h r l A Cylinder With Cones On Its Ends NOTE- The cones are of the same dimensions Surface area of the model = CSA of the cylinder + CSA of both the cones = 2πrh + 2 π rl = 2πr ( h + l ) BACK

Slide 17: 

h r A Cylinder With Hemispherical Cavities Surface area of the model = CSA of the cylinder + CSA of the two hemispheres = 2πrh + 2 ( 2πr 2 ) = 2πrh + 4πr 2 = 2πr ( h + 2r ) BACK

Slide 18: 

Two Cubes Of Similar Dimensions a a a When two cubes are joined, they form a cuboid. In the given model when the two cubes of side ‘a’ are joined, we get a cuboid of dimension > l = a + a b = a h = a So the model’s surface area is 2 ( lb + bh +hl ) = 2 { ( a + a ) a + a 2 + a ( a + a) } = 2 ( 2a 2 + a 2 + 2a 2 ) = 2 ( 5a 2 ) = 10a 2 BACK

Slide 19: 

A Capsule h r r Surface area of the model = CSA of the cylinder + CSA of the two hemispheres of the same dimension = 2πrh + 2πr 2 + 2πr 2 = 2πrh + 4πr 2 = 2πr ( h + 2r ) BACK

Slide 20: 

Hemispherical Depression In A Cuboid Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere = 2 ( lb + hl + hb ) + 2 π r 2 – πr 2 = 2 ( lb + hl + hb ) + πr 2 BACK h b l r

Slide 21: 

A Cuboid Surmounted By A Hemisphere Surface area of the model = TSA of the cuboid + CSA of the hemisphere - CSA of the top of the hemisphere = 2 ( lb + hl + hb ) + 2 π r 2 – πr 2 = 2 ( lb + hl + hb ) + πr 2 h b l r BACK

Slide 22: 

BACK A Hollow Cylinder Surmounted By A Hemisphere h r r Surface area of the model = CSA of the cylinder + CSA of the hemisphere = 2πrh + 2πr 2 = 2πr ( h + r )