SURFACE AREA AND VOLUME

Holiday homework

INTRODUCTION• Here’s a quick recap of what are plane figures and solid figures.

• Figures that can be drawn easily on a plane surface such as blackboard or notebook are said to be Plane Figures. Some of these figures include Rectangles, Square, Triangles and the list goes on...

• Figures formed when more than one plane figures are complied over each other in such a manner that they form a three dimensional figures which includes Length, Breadth and Height. Some of these figures include cube, cuboid and many more.

• Major difference between them is this that plane figures only have Area Perimeter but Solid figures have Area as well as, Volume.

• We are going to talk about Solid figures only.

CUBOID ( FORMED FROM RECTANGLE)

This is what a cuboid looks like

It has got three sides (Three Dimensional Figure)

l=length, b=breadth, h=height

Lets talk about its area.

A three dimensional figures has got two kind of areas

i. Total surface area (T.S.A)

ii. Lateral surface area (L.S.A)

CUBOID’S AREAA cuboid has 6 rectangles in it, which means area of all 6 rectangles = area of a cuboid.

Hence total surface area = area of rectangle= 6(b*h)

2(lb)+2(bh)+2(lh)

2(lb+bh+hl)

Lateral surface includes the area of 4 faces instead of 6 faces

hence, lateral surface area = 2(lh+2(bh) or 2(l+b)h

Cuboid

CUBE ( FORMED FROM SQUARE)The cube is a three dimensional figure formed from square.

Therefore all the sides say ‘a’ are equal in area. There is no need to differentiate between length, height or breadth because all are same.

Total surface area of a cube is area of 6 square = 6a^2

Similarly lateral surface area of a cube = area of 4 squares= 4s^2

EASIEST THREE DIMENSIONAL FIGURE ATLEAST FOR ME……..

CUBE

CYLINDER(FORMED FROM CIRCLES)

CYLINDER IS A SOLID FIGURE WHICH COMPRISES OF TWO CIRCLES AT THE TOP AND AT THE BOTTOM AND HAS HEIGHT AS WELL AS RADIUS

NOW LETS HAVE A LOOK HOW THE TOTAL SURFACE AREA AND LATERAL SURFACE AREA CAN BE FOUND.

TOTAL SURFACE ARE MEANS THE WHOLE OF THE TOP BOTTOM AND MIDDLE.

SO TOP AND BOTTOM ARE CIRCLES SO IT IS AREA OF CIRCLE *2 AS THERE ARE TWO AS TOTAL.

THE LEFT OVER PART CAN BE SAID AS THE CIRCUMFERENCE OF THE CIRCLE SO, 2R AND H IS THE HEIGHT OF CYLINDER. HENCE

TOTAL SURFACE AREA BECOMES +

CURVED SURFACE AREA IS JUST THE CIRCUMFERENCE*HEIGHT = CYLINDER

CONECone has no uniform cross-section and can be said as the most complicated one.

It has got slant height radius and length.

The lateral surface area of a cone is the area of the lateral or side surface only

So, the formula for the lateral surface area of a right cone is L. S. A. = πrl, where l is the slant height of the cone. 

TSA( Total surface area) = The formula for the total surface area of a right cone is T. S. A. = πrl + πr2.

SPHRE AND HEMISHPERE

Hemisphere is a figure which is formed when hemisphere is divided from the very middle.

Surface area of sphere =4*area of circle which makes it 4

Lateral surface area of hemisphere= same as the total surface area

Total surface area of hemisphere = 3

Lateral surface area of hemisphere= half the area of sphere which makes it 2

VOLUME OF SOLID FIGURES

• Volume is just the measure of the space occupied.

• The figures which were discussed earlier we are going to discuss about them only but this time how to find their holding capacity.

• Lets start off with cuboid.

• The area of plane region occupied by each rectangle*height = measure of space occupied by cuboid.

• So we get A*h= V or volume= l*b*h

• Next on line is cube.

• Volume of cube= edge*edge*edge = a^3

• NOTE: FIGURES SUCH AS CUBOID AND CUBE HAS THE VOLUME = LENGTH*BREADTH*HEIGHT

CONTINUEVolume of cylinder = base area*height = area of

circular base*height

Volume of cylinder=

• Volume of sphere =4/3 Volume of hemisphere = half the sphere = 2/3

• Volume of cone = 1/3h