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THE PRESENTATION BEGINS

UMESH SIRUMESH SIR

INTRODUCTION CUBE CUBOID RIGHT CIRCULAR CYLINDER RIGHT CIRCULAR CONE SPHERE HEMISPHERE

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 milk? If so, then you've filled the volume of a

glass with milk. 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 surfaces.

For example : The amount of paper required to wrap a gift gives us an idea of surface area of gift.

Volume of a solid object refers to the amount of space it occupies or contains.

For example : The amount of water a swimming pool can hold gives us an idea of the volume of the swimming pool.

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.

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 C.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

= 4 πr2

Volume of sphere = 4 πr3

3

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