What is in here: Cubolid Cube Cylinder Cone Sphere Hemisphere Conversion of units Difference between Capacity & Volume

1. Volume And Surface
Area
IX C

2. CONTENTS
CUBOID
CUBE
CYLINDER
CONE
SPHERE
HEMISPHERE

3. CUBOID

4. To find the surface area of a shape, we
calculate the total area of all of the faces.
A cuboid has 6 faces.
The top and the bottom of
the cuboid have the same
area.
Surface area of a cuboid

5. To find the surface area of a shape, we
calculate the total area of all of the faces.
A cuboid has 6 faces.
The front and the back of
the cuboid have the same
area.
Surface area of a cuboid

6. To find the surface area of a shape, we
calculate the total area of all of the faces.
A cuboid has 6 faces.
The left hand side and the
right hand side of the
cuboid have the same
area.
Surface area of a cuboid

7. We can find the formula for the surface area of a
cuboid in the way which is shown below.
Surface area of a cuboid =
Formula for the surface area of a cuboid
h
l
b
2 × lb Top and bottom
+ 2 × hb Front and back
+ 2 × lh Left and right side
= 2lb + 2hb + 2lh
= 2( lb + bh + lh )

8. 10 cm
4 cm
6 cm
VOLUME OF A CUBOID
Look at this cuboid.
Now imagine it is full of
cubic centimetres.
Can you see that there are 10  4 = 40 cubic centimetres on the
bottom layer?
There are 6 layers of 40 cubes making 40  6 = 240 cm3
1 cm3

9. 10 cm
4 cm
6 cm
VOLUME OF A CUBOID
length
breadth
height
When we worked out the volume, we multiplied the length by the breadth
and then by the height.
Volume of a cuboid = length  breadth  height
or
V = l b h

10. 10 cm
4 cm
6 cm
V = l b h
= 10  4  6 cm3
= 240 cm3
Lets us look
again at the
same cuboid
and this time
try the
formula.

11. CUBE

12. How can we find the surface area of a cube of length a?
Surface area of a cube
x
All six faces of a cube have the same area.
The area of each face is a × a = a2
Therefore,
Surface area of a cube = 6a2

13. Volume of a cube
Volume of a cube is calculated by
A cube is a cuboid with all the edges (a) equal.
Volume of a cube = lbh
Volume of a cube = a3
V = (4 x 4) x 4
= 64 m3

14. Cylinder

15. This will happen if we unrolled
and removed the end of a
cylinder….
h
2Πr2
C.S.A = Area of the
rectangle
= 2Πr2 X h
= 2Πr2h

16. Notice that we had formed 2 circles
and a 1 rectangle….
The 2 circles serves as our bases of
our cylinder and the rectangular
region represent the body

17. This is the formula in order to find
the surface area of a cylinder.
T.S.A. = Area of 2 circular bases +
Area of the rectangle
T.S.A = 2πr2 + 2πrh
T.S.A = 2πr(r+h)

18. Volume of A cylinder
Volume of a cylinder = Area of the base
area x height
= πr2 x h
= πr2h

19. CONE

20.  A cone has a circular base and a vertex that is not in the
same plane as a base.
 In a right cone, the height meets the base at its center.
 The height of a cone is the perpendicular distance between
the vertex and the base.
 The slant height of a cone is the distance between the
vertex and a point on the base edge.
Height
Lateral Surface
The vertex is directly
above the center of
the circle.
Base
r
Slant Height
r

21. Surface Area of a Cone
C.S.A = πrl
T.S.A = πr2 + πrl
l
r
h

22. Comparing Cone and Cylinder
• Use plastic space figures.
• Fill cone with water.
• Pour water into cylinder.
• Repeat until cylinder is full.
r r
h

23. Volume of Cone
• 3 cones fill the cylinder, so…
• Volume = ⅓ Base Area x height
Volume = 1/3 πr2h
=

24. SPHERE

25. Surface Area of a Sphere
Surface Area of a Sphere
= 4πr2

26. Volume of a Sphere
Using relational solids and pouring material we noted that the volume of a
cone is the same as the volume of a hemisphere (with corresponding
dimensions)
Using math language Volume (cone) = ½ Volume (sphere)
Therefore 2(Volume (cone)) = Volume (sphere)
=
OR
+

27. 2(Volume (cone)) = Volume (sphere)
2( ) (height) /3= Volume (sphere)
2( )(h)/3= Volume (sphere)
BUT h = 2r
2(r2)(2r)/3 = Volume(sphere)
4 ( r3)/3 = Volume(sphere)
Volume of a Sphere
Area of Base
r2
2 X
=
h
r
r

28. HEMISPHERE

29. Surface area of hemisphere
Total surface area of a hemisphere:
3Пr 2
Curved surface area of a hemisphere:
2Пr 2

30. Volume of hemisphere
Volume of a hemisphere:
2/3 Пr 3

31. CONVERSION OF UNITS

32. Conversion of units
• 1cm =10mm
• 1m = 100cm
• 1km = 1000m

33. Conversions of Units
1 cm2 = 10 mm x 10 mm =100 mm2
1 m2 = 100 cm x 100 cm = 10 000 cm2
1 m2 = 1000 mm x 1000 mm = 10 00 000 mm2

34. CUBIC UNITS
• 1 cm3
• = 1cm x 1cm x 1cm
• = 10 mm × 10 mm × 10 mm
• = 1000 mm3
• 1 m3
• = 1m x 1m x 1m
• = 100 cm × 100 cm × 100 cm
• = 1 000 000 cm3

35. VOLUME
• The volume of three-
dimensional figure is
the amount of space
within it.
• Measured in cubic
unit.
CAPACITY
• Capacity is the
amount of material
usually liquid) that a
container can hold.
• Measured in
millilitres, litres and
kilolitres.
Volume and capacity are related.

36. How does Volume relate to Capacity?
• 1000 mL = 1 L
• 1000 L = 1 kL
• 1 cm3 = 1 mL
• 1000cm3 = 1000ml = 1L
• 1 m3 = 1000 L = 1 kL

37. Examples of Capacity

39. Achieved by
Violet Black