Surface area and volume

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

Success criteria : I will be able to
•solve problems that involve relating a shape’s volume
to its surface area.
•solve problems that involve volume and surface area
calculations.

The big idea video

Let’s watch it together

https://youtu.be/iZurDlFHq
GM?si=VWY96Cn4GBYN9t
JX

 Vertices, Faces and Edges are the three properties that define any three-

dimensional solid.

 A vertex is the corner of the shape whereas a face is a flat surface and an

edge is a straight line between two faces.

 3d shapes faces, edges and vertices, differs from each other.

Cube is a solid shape, which has 6 faces. A cube is one of the
simplest shapes in three-dimensional space. All the six faces of a
cube are squares, a two-dimensional shape.

surface area of a given cube states that if the total surface area is equal to the
sum of all the areas of the faces of the cube. Since the cube has six faces,
therefore, the total surface area of the cube will be equal to sum of all six faces
of cube.

Surface area or total surface area of a cube (T.S.A) = 6s2


Lateral surface area of cube is the surface area covered by the four faces of a
cube, except its top and bottom faces.


The lateral surface area of a cube is equal to the sum of the areas of four faces
of a cube.

Lateral surface area of a cube (L.S.A) = 4s2

Multiple Choice

What is the lateral surface area (LSA) of a Rubik's cube of side length 4
centimetre?

• 16 square centimetres
• 36 square centimetres
• 100 square centimetres
• 64 square centimetres

The volume of a cube defines the number of cubic units, occupied by the cube
completely. The unit of volume of the cube is in cubic units such as centimeters3,
meters3, inches3, feet3, etc.
Volume is nothing but the total space occupied by an object.

Volume = side x side x side = s3

Multiple Choice

Find the volume of the cube, having the sides of
length 7 cm.

• 98 cubic cm
• 49 cubic cm
• 343 cubic cm
• 240 cubic cm

Multiple Choice

Find the volume of cube with edge-length equal
to 11 feet.

• 1331 cubic feet
• 121 cubic feet
• 144 cubic feet
• 110 cubic feet

Drag and Drop

Find the length of the edges of the cube, if its
volume is equal to 125 cm³.​

​ length of the edges of the cube =​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

7cm

4cm

3cm

5cm

Multiple Choice

1. How to find the total surface area of cube?
2. What is the volume of a cube?
3. What is the lateral surface area of cube?

• Total surface area of cube = 4 * (side length)^2
• 1. Total surface area of cube = 6 * (side length)^2. 2. Volume of cube = (side length)^3. 3. Lateral surface area of cube = 4 * (side length)^2.
• Volume of cube = 2 * (side length)^3
• Lateral surface area of cube = 3 * (side length)^2

 A cuboid is a three dimensional solid that has

6 faces (rectangular), 8 vertices and 12 edges.

 A cuboid has three dimensions such as length,

width and height.

 A perfect cuboid is said to be a cuboid that has

integer edges..

The Total surface area of a cuboid (TSA) is equal to the sum of the areas of
it’s 6 rectangular faces.

Total Surface Area of a Cuboid (TSA) = 2 (lb + bh + lh)

AREA OF RECTANGLE 1 = (l x h) +
AREA OF RECTANGLE 2 = (l x b) +
AREA OF RECTANGLE 3 = (l x h) +
AREA OF RECTANGLE 4 = (l x b) +
AREA OF RECTANGLE 5 = (b x h) +
AREA OF RECTANGLE 6 = (b x h)

= 2 (l x b) + 2 (b x h) + 2(l x h)

= 2 (lb + bh + hl)

The lateral surface area (LSA) of a cuboid is the sum of the areas of its four
side faces, excluding the top and bottom faces.

L.S.A of a cuboid = 2 ( l + b) x h

 Volume is the space occupied by an object.

 Volume is also referred to capacity of an object.

VOLUME OF CUBOID = BASE AREA x HEIGHT

= (l x b) x h
= l x b x h

Volume of a cuboid = l x b x h

Multiple Choice

find the amount of air that can be accumulated in a room that has a length of 5m, breadth of 6 m and a height of 10 m.

• 50 cubic meters

• 300 cubic meters
• 60 cubic meters
• 150 cubic meters

Multiple Choice

Find the area of the cardboard required to make a closed box of length 25 cm, 0.5 m and height 15 cm.

• The area of the cardboard required to make the closed box is 2500 square centimeters.
• The area of the cardboard required to make the closed box is 2150 square centimeters.
• The area of the cardboard required to make the closed box is 1500 square centimeters.
• The area of the cardboard required to make the closed box is 1800 square centimeters.

Multiple Choice

A classroom is 11 m long, 8 m wide and 5 m high. Find the sum of the areas of its floor and the four walls (including doors, windows etc.)

• 168 sq. m
• 180 sq. m
• 194 sq. m
• 206 sq. m

Open Ended

1.What is the difference between total surface area and the lateral surface area?

2.How do you find the surface area and volume of a cuboid?
3. What is the lateral surface area of a cuboid?

Cylinder is one of the basic 3d shapes, in geometry, which has
two parallel circular bases at a distance. The two circular bases
are joined by a curved surface, at a fixed distance from the
center. The line segment joining the center of two circular bases
is the axis of the cylinder. The distance between the two circular
bases is called the height of the cylinder.

 The surface area of a cylinder is the area occupied by its surface in a

three-dimensional space.

 The cylinder area is defined as the sum of the curved surface and the area

of two circular bases of the cylinder.

Total surface area = 2πr (h + r)

The area of the curved surface of the cylinder which is contained
between the two parallel circular bases. It is also stated as a
lateral surface area.

Curved Surface Area = 2πrh

The volume of a cylinder is the density of the cylinder which
signifies the amount of material it can carry or how much
amount of any material can be immersed in it.

Volume (V) =

Multiple Choice

Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 14cm and height is 20 cm.

• Curved surface area = 700 cm^2, Total surface area = 1000 cm^2
• Curved surface area = 800 cm^2, Total surface area = 1100 cm^2
• Curved surface area = 950 cm^2, Total surface area = 1350 cm^2
• Curved surface area = 880 cm^2, Total surface area = 1232 cm^2

Open Ended

find the volume of this cylinder with radius of the base 7 cm and perpendicular height 10 cm.​

1. Surface area of a solid is the sum of the areas of its faces.
2. Surface area of

a cuboid = 2(lb + bh + hl)
a cube = 6S2
a cylinder = 2πr(r + h)

3. Amount of region occupied by a solid is called its volume.
4. Volume of

a cuboid = l × b × h
a cube = S3
a cylinder = πr2h

it's time to solve

Nothing is more powerful for your future than being a gatherer of good ideas and information. That's called doing your homework​

Open Ended

The length, breadth, and height of a room are 5 m, 4 m and 3 m
respectively. Find the cost of white washing the walls of the room and the
ceiling at the rate of AED 7.50 sq.m.

Multiple Choice

What will happen to the volume of a cube, if its edge is

(i) halved (ii) trebled?

• The volume will remain the same if the edge is halved or trebled
• The volume will be 1/8 of the original volume if the edge is halved, and 27 times the original volume if the edge is trebled.
• The volume will be doubled if the edge is halved
• The volume will be halved if the edge is trebled

Open Ended

A company packages its milk powder in cylindrical container whose base
has a diameter of 14 cm and height 20 cm. Company places a label around the
surface of the container (as shown in the figure). If the label is placed 2 cm
from top and bottom, what is the area of the label.