This is a presentation about Grade 9 Mathematics concept - Surface areas of cube, cuboid, cylinder and cone.

1. Digital Plan - 2
Preliminary Information
Name: B S D
Roll No.: 1642-22
Subject: Mathematics
Class: IX
Topic: Surface Areas
Duration: 45 min
Method: Digital Plan

2. Academic Standards
1. Problem Solving – Student will be able to solve problems based on
surface areas
2. Reasoning Proof – Students will be able to ask for reasoning and
proof of how the surface areas are calculated for different 3D shapes
3. Communication – Students will be able to communicate the
definitions of Cuboid, cube, cylinder and cone
4. Connection – Student will be able to connect the formulae to the
real-life objects
5. Visualization and Representation – Student will be able to visualize
the different sides of 3D shapes and represent them accordingly

3. Surface Areas

4. Content Analysis
• Surface area of Cuboid
• Surface area of Right Circular Cylinder
• Surface area of Cube
• Surface area of Right Circular Cone
• Curves surface area of a Cone
• Examples

5. Cuboid
In our day-to-day life ,we come across
objects like a Wooden box, a Match box, a
Tea packet ,a Chalk box, a Dice , a Book
etc. All these objects are made of six
rectangular plane regions. These objects
are in the shape of a cuboid.
Definition- “Cuboid is a solid bounded by
six rectangular plane regions”.

6. Surface Area of a Cuboid
• Lateral surface area of a cuboid is the sum of
areas of four of its faces, leaving the top and
bottom faces.
i.e, sum of lh, lh, bh and bh, which is, 2lh +
2bh.
• Therefore, lateral surface area of a cuboid of
length l, breadth b and height h is equal to
'2lh + 2bh' or '2(l + b)h’.
• The formula for the total surface area of a
cuboid is : TSA = 2 (lb + bh + lh) square units.

7. Surface Area of Right circular Cylinder
• Consider a right circular cylinder of radius “r”and height
“h”Area of the lateral surface of the cylinder=Area of the
rectangle= l * b= 2Πr * h= 2 Π r h square unitsb=hl=2Πr
• Surface area of cylinder = Area of rectangle= 2 π r h
Other method of Finding Surface area of cylinder with the
help of paperr hL=2πrB=hSurface area of cylinder = Area of
rectangle= 2 π r h
• Thus , for a cylinder of radius “r” and height “h” ,
we have L.S.A = 2 Π r h square units. Each base Area = Π
r2Total Surface Area = (2 Π r h + 2Π r2 )= 2 Π r (h + r ) Square
units

8. Area of Top face EFGH = (l * b)cm2
Area of Bottom face ABCD =(l*b)cm2
Area of Side face AEHD =(b*h)cm2
Area of Side face BFGC = (b*h)cm2
Area of Front face ABFE = (l*h)cm2
Area of Back face DHGC = (l*h)cm2
Total surface Area of the Cuboid = sum of the areas of all
its six faces = lb+lb+bh+bh+lh+lh = 2lb+ 2bh + 2lh
= 2(lb+bh+lh) cm2

9. Surface Area of a Cube
“A cuboid whose length, breadth and height are all equal , is called a
cube”
Surface area of a cube = 2(a*a + a*a + a*a) = 2(a2 + a2 + a2) = 6 a2

10. Examples…
Example 2) Find the surface Area of
a cube whose edge is 11 cm
Solution) Here l=11cm
surface area of the given cube =
6l2=6 (11)2 cm2= 6 * 121
Cm2=726 cm2
Example 1) Find the Surface Area
of a match box whose length ,
breadth and height are 16 cm,8cm
, and 6 cm respectively.
Solution) since match box is in the
form of a cuboid. Here l=16 cm ,
b= 8 cm , h= 6 cm
Surface Area of Match Box=2(lb +
bh + lh)=2(16*8+8*6+16*6)
cm2=2( ) cm2=544cm2
Example 3) Three cubes each of side 5
cm are joined end to end. Find the
surface area of the resulting cuboid.
Solution)The dimension of the cuboid
so formed are as under l=15cm ,
b=5cm , h=5cm
Surface Area of cuboid= 2(lb + bh +
lh)= 2( ) cm2= 350 cm2

11. Total Surface area of a solid cylinder
Curved surface=area of two circular surfaces
Area of curved surface += (2 π r) x( h) + 2 π r2= 2 π r (
Example1)
The curved surface area of a right circular cylinder of
height 14 cm is 88 cm2. Find the diameter of the base of
Solution) Let r be radius and h be the height of the
142 * 22/7 * r * 14 = 8888 r = 88r = 1Diameter of the

12. Surface area of a Right Circular cone
• Curved surface Area of the
cone = Area of the sector
• Curved surface Area of the
cone = Area of the sector
• VAB= ½ * ( arc length *
radius)
= ½ * 2 π r * l
= π r lC.S.R = ½ *
(circumference of base * slant
height)

13. Curved Surface Area of a Cone
• Curved Surface Area of a Cone = 1 / 2 * l * 2 Π r=
Π r l
• Total Surface Area of a cone = Π r l + Π r2= Π r ( l
+ r)
• Example 1)The diameter of a cone is 14cm and
its slant height is 9 cm. Find the area of its curved
surface .
• Solution) S = Π r l
• Here , r = 14/2 cm and l = 9 cms
= 22/7 * 7 * 9 cm2
= 198 cm2