surface area and volume by chandan kumar sethy , class - 10th

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AMIT KU.BHATANAGARAMIT KU.BHATANAGAR

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.

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.

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

VOLUMEVOLUME Volume of a cube of edge a units is a3 cubic units.

(side)³

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

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

VOLUMEVOLUME Volume of a cuboid =Length × Breadth × Height Or V = l × b × hWhere, V = volumel = length, b = breadthh = height

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.

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)

VOLUMEVOLUME Volume of a

cylinder = Area of base ×

height = πr2h

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

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

TOTAL SURFACE TOTAL SURFACE AREAAREA T.S. A. of Cone = C.S.A. +

Base Area = πrl + πr2

= πr (l +r)

2B rr

VOLUMEVOLUME Volume of Cone = 1 × Volume of

Cylinder 3 = 1 × πr2h

3

SURFACE SURFACE AREA AND AREA AND VOLUMEVOLUME Surface area of sphere

= 4πr2

Volume of sphere = 4πr3

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

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

Volume Of A Frustum:Volume Of A Frustum:1/3 1/3 ППh(rh(r 2 2+R+R 2 2+Rr)+Rr)