surface area and volume by chandan kumar sethy , class - 10th
TRANSCRIPT
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AMIT KU.BHATANAGARAMIT KU.BHATANAGAR
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INTRODUCTIOINTRODUCTION:-N:-
Have you ever wrapped a birthday gift? If so, then you've covered the surface area of a polyhedron with wrapping paper. Have you ever poured a glass of apple juice? If so, then you've filled the volume of a glass with apple juice. Not only this, but in day-to-day life, we come across many activities which involve the concept of surface areas and volume.
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Surface Area of an object refers to the total area of all its sides.
Lateral Surface Area of an object refers to the total area excluding its base and top.
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SURFACE SURFACE AREAAREA
If each edge of cube is a units, itsTotal surface area = 6a2 sq. units
Area of the faces leaving the topAnd the bottom ones is known asIts L.S.A. (Lateral Surface Area).
L.S.A. of cube = 4a2 sq. units
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VOLUMEVOLUME Volume of a cube of edge a units is a3 cubic units.
(side)³
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TOTAL SURFACE TOTAL SURFACE AREAAREA Surface area of a
cuboid =2 × lb Top and bottom
+ 2 × bh Front and back
+ 2 × lh Left and right side
= 2(lb + bh + lh)
h
l b
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LATERAL SURFACE LATERAL SURFACE AREAAREA L.S.A. of cuboid
= T.S.A. – Area of top and base
= 2(lb + bh + lh)–2(lb)
= 2 (bh + hl) = 2 (l+b) × h
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VOLUMEVOLUME Volume of a cuboid =Length × Breadth × Height Or V = l × b × hWhere, V = volumel = length, b = breadthh = height
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WHAT IS A RIGHT WHAT IS A RIGHT CIRCULAR CIRCULAR CYLINDER CYLINDER ?? A cylinder is a
right circular cylinder if :
Its base is a circle and
Radius of the base is perpendicular to its height.
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SURFACE AREASURFACE AREA L.S.A. of cylinder = Area of
rectangular sheet = 2πrho T.S.A. of cylinder = C.S.A. + Lid
area + Base area = 2πrh + πr2 +
πr2
= 2πr (h+r)
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VOLUMEVOLUME Volume of a
cylinder = Area of base ×
height = πr2h
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WHAT IS A RIGHT WHAT IS A RIGHT CIRCULAR CONE?CIRCULAR CONE? In a right
circular cone, the radius of the circular base is perpendicular to its height.
Also, Slant Height
l =
Height h
Baser
Slant Height l
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CURVED SURFACE CURVED SURFACE AREAAREA
l l
2πr
r
Area of sector = Circumference of arc
Area of circle Circumference of circle
Area of sector = 2πr × πl 2 = πrl 2πl
C.S.A. of cone = Area of sector = πrl
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TOTAL SURFACE TOTAL SURFACE AREAAREA T.S. A. of Cone = C.S.A. +
Base Area = πrl + πr2
= πr (l +r)
2B rr
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VOLUMEVOLUME Volume of Cone = 1 × Volume of
Cylinder 3 = 1 × πr2h
3
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SURFACE SURFACE AREA AND AREA AND VOLUMEVOLUME Surface area of sphere
= 4πr2
Volume of sphere = 4πr3
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SURFACE SURFACE AREA AND AREA AND VOLUMEVOLUME C.S.A. of hemisphere = 2πr2
T.S.A. of hemisphere = C.S.A. + Base Area
= 2πr2 + πr2
= 3πr2
Volume of hemisphere = 2 πr3 3
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Total Surface Area Of A Frustum:Total Surface Area Of A Frustum:П(r+R)l + П(r+R)l + ППrr 2 2 + + ППRR 2 2
=П(r+R)l + =П(r+R)l + ПП(r(r 2 2+ R+ R22))Curved Surface Area Of A Frustum:Curved Surface Area Of A Frustum:
П(r+R)lП(r+R)l
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Volume Of A Frustum:Volume Of A Frustum:1/3 1/3 ППh(rh(r 2 2+R+R 2 2+Rr)+Rr)
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