Surface Areas -- FORMULAE --

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

CUBE MAIN MENU NEXT CUBE a a a a Surface Area We will need to find the surface area of the top, base and sides. Area of the top and bottom is 2a2 Area of sides (CSA) is 4a2 Therefore the formula is: 6a2 Volume V = a 3 a a a a MAIN MENU NEXT

CUBOID MAIN MENU NEXT 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

CONE TSA = תr(s+r) NEXT MAIN MENU

CYLINDER CSA = 2πr2 NEXT MAIN MENU

SPHERE NEXT MAIN MENU

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

SURFACE AREA OF A COMBINATION OF SOLIDS MAIN MENU NEXT

SURFACE AREA OF A COMBINATION OF SOLIDS

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

A Solid Cylinder With A Conical Cavity Surface Area of the model = CSA of the cylinder + CSA Of the cone + Area of the cylinder’s base = 2πrh + πrl + πr2 = πr ( 2h + l + r ) h l r

Surface Area of the model = CSA of hemisphere + CSA of the cone A Sphere Attatched To A Cone Surface Area of the model = CSA of hemisphere + CSA of the cone = 2πr2 + πrl = πr ( 2r + l ) l r

Surface area of the sphere – Area of the cylinder’s base A Round Bottom Flask r Surface area of the model = CSA of the cylinder + Surface area of the sphere – Area of the cylinder’s base = 2 πrh + 4 πr2 – πr2 = πr ( 2h – r ) + 4πr2 h 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 + 2πR2 + 2πrh + 2πr2 – πr2 = 2πR ( H + R ) + 2πr ( h + r ) H R

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

Surface area of the model = CSA of the cylinder A Cylinder With Hemispherical Cavities Surface area of the model = CSA of the cylinder + CSA of the two hemispheres = 2πrh + 2 ( 2πr2 ) = 2πrh + 4πr2 = 2πr ( h + 2r ) h r

Two Cubes Of Similar Dimensions 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 a a So the model’s surface area is 2 ( lb + bh +hl ) = 2 { ( a + a ) a + a2 + a ( a + a) } = 2 ( 2a2 + a2 + 2a2 ) = 2 ( 5a2) = 10a2 a

A Capsule = 2πrh + 4πr2 = 2πr ( h + 2r ) Surface area of the model = CSA of the cylinder + CSA of the two hemispheres of the same dimension = 2πrh + 2πr2 + 2πr2 = 2πrh + 4πr2 = 2πr ( h + 2r ) r r h

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 ) + 2πr2 – πr2 = 2 ( lb + hl + hb ) + πr2 r h b l

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 ) + 2πr2 – πr2 = 2 ( lb + hl + hb ) + πr2 r h b l

Surface area of the model = CSA of the cylinder A Hollow Cylinder Surmounted By A Hemisphere r Surface area of the model = CSA of the cylinder + CSA of the hemisphere = 2πrh + 2πr2 = 2πr ( h + r ) h r

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