MATHS PROJECT ON THE TOPIC

MATHS PROJECT ON THE TOPIC

Surface Areas And Volumes

Acknowledgement

I would like to express my special thanks of gratitude to my teacher (name of the teacher), who gave me the golden opportunity to do this

wonderful Project, which also helped me in doing a lot of Research and I came to know about so many

new things.I am really thankful to them.

Secondly i would also like to thank my parents and friends who helped me a lot in finishing this project

within the limited time.I am making this project not only for marks but to also

increase my knowledge .THANKS AGAIN TO ALL WHO HELPED ME.

Surface AreaSurface area is the total area of the faces and curved

surface of the a solid figure. Mathematical description of the surface area is considerably more involved than the definition of arc length the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere,

are assigned surface area using their representation as

parametric surfaces.

This definition of the surface area is based on methods of infinitesimal calculus and involves 

partial derivatives and double integration.

VOLUMEVolume is the measure of the amount of space inside of a

solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic", that is, the number of little element

cubes that fit inside the figure. The formula for the volume of a rectangular prism is:

Area = l x w x hwhere:

l = lengthw = widthh = height

Surface area of Cuboid

Close Cuboid

Open CuboidAND

1

2

3

4

5 6

•In Open Cuboid -

•Area of rectangle 1= (l * h) +

•Area of rectangle 2= (l * h) +

•Area of rectangle 3= (l * b) +

•Area of rectangle 4= (l * b) +

•Area of rectangle 5= (h * b) +

•Area of rectangle 6= (h * b)

=2(l*b) + 2(h*b) + 2(l*h)=2(lb + bh + lh)

Surface area of the cuboid

This shows that

2(lb+bh+lh) sq units

This shows that

Surface area of the cuboid

Volume of a cuboid

• Base area = l*b• Height = h• So, volume of a

cuboid = l * b * h =lbh cubic units

Diagonal of the cuboid

= square root of l2 + b2 + h2

Area of four walls of a room = lh + lh + bh + bh =

2(l+b)h sq. units

Close Cube

AND

Open Cube

Surface area of Cube

•Area of sq. 1 = a * a•Area of sq. 2 = a * a

•Area of sq. 3 = a * a•Area of sq. 4 = a * a

•Area of sq. 5 = a * a•Area of sq. 6 = a * a

In open cube -

Surface area = Area of all 6 faces = 6a*a

THIS SHOWS

THAT

Surface area of a cube

= 6a*a sq units

Volume of a cube

a*a*a cubic unit

Curved surface area of a CYLINDER=2(pie)rh

=2 (pie)r*h=perimeter of base * height

Total surface area = Curved surface area + Area of circular ends=2 (pie)rh + 2 (pie)r*r

=2 (pie)r (h + r)

VOLUME OF CYLINDER

Curved surface area of HOLLOW CYLINDER= external S.A + internal S.A= 2(pie)Rh +2 (pie)rh= 2(pie)h (R + r)

Total surface area= 2(pie)Rh +2

(pie)rh + 2[(pie) R*R – (pie) r*r

= 2(pie)h(R + r) +2 (pie)(R + r)(R – r)

= 2(pie)h(R + r) (R + h – r)

VOLUME OF MATERIAL

= external vol. – internal vol.= (pie)R*Rh - (pie)r*rh

= (pie)h(R*R – r*r)

Curved surface area of right circular cone= (pie) r l sq. units

Total surface area of cone= C.S.A + Area of base

= (pie)rl + (pie)r*r= (pie)r(l + r) sq. units

Volume of CONE

= 1/3 (pie)r*rh

= 1/3(ar. Of the base)* height