This PPT features a well explained theory / concepts / derivations of the formula of Surface Area of various 3D shapes : like cube, cuboid and cylinder with the help of expanded 3D shapes (called "nets").
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Surface Area (ORANGE THEME)
1.
2. This shows that the outer surface of a cube is made up of
six squares but in fact they are the faces of cube. So,
Surface area of cube = Area of all six squares
Surface area of cube = a2 + a2 + a2 + a2 + a2 + a2
Surface area of cube = 6a2
3. This shows that the lateral or curved surface of a cube is
made up of four squares. So,
Lateral or curved surface area of cube = Area four squares
Lateral or curved surface area of cube = a2 + a2 + a2 + a2
Lateral or curved surface area of cube = 4a2
4. This shows that the outer surface of a cuboid is made up of
six rectangles but in fact they are the faces of cuboid. So,
Surface area of cuboid = Area of all six rectangles
Surface area of cuboid = (lb)+(lb)+(bh) +(bh) + (hl) +(hl)
Surface area of cuboid = 2(lb)+2(bh)+2(hl)
Surface area of cuboid = 2(lb+bh+hl)
5. This shows that the lateral or curved surface of a cuboid is
made up of four rectangles. So,
Lateral or curved surface area of cuboid = Area of four
rectangles
Lateral or curved surface area of cuboid
=(bh)+(bh)+(hl)+(hl)
Lateral or curved surface area of cuboid = 2(bh)+2(hl)
Surface area of cuboid = 2(l+b)h
6. This shows that the outer surface of a cylinder is made up
of one rectangle and two circles. So,
Surface area of cylinder = Area of rectangle + Area of two
Circles
Surface area of cylinder = 2 תrh + ( תr2 + תr2 )
Surface area of cylinder = 2 תrh + 2(תr2)
Surface area of cuboid =2 תr(r+h)
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7. This shows that the lateral or curved surface of a cylinder
is made up of one rectangle. So,
Lateral/curved surface area of cylinder = Area of rectangle
Lateral/curved surface area of cylinder = 2 תrh
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