1. The document discusses surface areas and volumes of solid geometric shapes, both individually and in combinations. It defines key terms like surface area, volume, and lateral surface area. 2. Methods are provided for calculating the surface area and volume of basic solids like cubes, cylinders, cones, and spheres. It also addresses calculations for composite solids made of combinations of these shapes. 3. The document explains that when solids change shape, or are combined, their total volume remains the same while surface area may change. Examples of converting shapes like candles and cutting watermelons are given.

1. By
Sri.Siddalingeshwara BP M.Sc, B.Ed, (P.hd)
SURFACE AREAS AND VOLUMES
Chapter-13
For
Class-X

2. Content:
1.Introduction
Plane and solid figures.
Definition of surface area and volume
Finding the Surface area and volume of a
solid figure
2.Surface Areas of a combination of solids
3.Volume of a combination of solids
4. Conversion of solid from one shape to another
5. Frustum of cone

3. 1.INTRODUCTION:
*. From class IX, you are familiar with some of the
cuboid, cube, cone, cylinder and sphere. As shown in
the figure.
*And also known about the finding the surface areas
and volumes of the above.
• Generally The above geometrical figures known as
solid figures
• Why they called solid figures?
• And what is the difference between plane and solid
geometrical figures?
Cuboid

7. Finding the Surface area and volume
1. Finding the Surface area and Volume of Cuboid

8. Note:
1.The total surface area of a solid is the sum of the areas of all of
the faces or surfaces that enclose the solid. The faces include the
tops and bottoms (bases) and the remaining surfaces.
2.The lateral surface area of a solid is the surface area of the
solid without the bases. for a cube, the lateral surface area would
be the area of four sides.
3. The Curved surface area of an object is the area of all the
curved surfaces in an object. For right circular cylinder the surface
joining the two bases of right circular cylinder is called its curved
surface
Cylinder
Cube

9. 2. Finding the surface area and volume of cube:
3. Finding the surface area and volume of cylinder: it consist of two circular ba
equal area in parallel planes, that are connected by a lateral surfaces that intersects the
Of the bases.

10. 4. Finding the surface area and volume of the cone:
(l)
(h)
(r)
5. Finding the surface area and volume of the sphere:
Slant height= 𝒓𝟐 + 𝒉𝟐

11.  Volume of the sphere:

12. Curved /Lateral
surface area of
solids

13. In this chapter will discusses about the combinations of
solid figures and Surface areas, Volume and Lateral
surface areas or Curved surface areas of the solid figures
.
For example:
In the above example, Truck with a container on its back carrying oil or water from
one place to another place It is in the shape of combination of solid figures.
i.e Cylinder with two hemispheres as it ends.

14. 2.Surface Areas of a combination of solids:
A composite solid is a solid made up of common
geometric solids
The total surface area of a combined solid is the sum of
the total surface areas of the individual solids that make
up the combined solid, excluding the overlapping parts
from each figure.
 Whereas the volume of a combined solid is the sum of
the volumes of the individual solids that make up the
combined solid.
.

15.  Example 1: let us consider truck as shown below
In the above example, Truck with a container on its back carrying oil or water from one
place to another place It is in the shape of combination of solid figures.
i.e Cylinder with two hemispheres as it ends.
So, The total surface area of the new solid is the sum of the curved surface areas of each
of the individual parts. This gives
TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of the other
hemisphere
Where: TSA = “Total surface area”
CSA = “ Curved surface area”

16. • Example 2: Hemisphere and a cone
 Find the surface area of the toy?
It’s a combination of solids . That is cone and hemisphere the
combine to form a Toy. As shown in the diagram.
it can be calculated by
Total area of the Toy= CSA of hemisphere + CSA of cone

17. 3.Volume of a combination of solids:
Volume is a physical quantity that measures the space
occupied by a solid. It is measured in cubic units. The volume
of a combination of solids given by adding up the volumes of
each individual solid - in the combination of solids. For
example, in a figure made up of a hemisphere and a cone
(like a top), the sum of the volumes of each solid gives us the
volume of the combination of solids.

18. 4. Conversion of solid from one shape to another:
When you convert one solid shape to another, it forms the other solid of
same ratio. its volume remains the same, no matter how different the new
shape is.
In fact,
 If you melt one big cylindrical candle to 5 small cylindrical candles, the
sum of the volumes of the smaller candles is equal to the volume of the
bigger candle.
 Cut a watermelon into slices, they are converting a solid shape into other
solid shapes. Regardless of the size and shape of the slices, there is one
fact that holds true of the whole process. The volume of all the slices
together exactly equals the volume of the original watermelon.
Convert a solid of a given shape to a solid of another shape, the surface
area usually changes. However, the volume is preserved.

19. Candles are generally in the form of cylinder. And some
candles shaped like an animal.
How They are made?
If you want a candle any special shape, you have to heat the
wax in a metal container till it becomes completely liquid .
Then you will have to pour it into another container which has
the special Shape that you want.
In a figure, From cylinder candle into to rabbit shaped candle
by melting the wax.
here, The volume of the new candle will be the same as the
volume of the earlier candle.

20. 1. A cylindrical pencil sharpened at one edge is the combination of
(A) a cone and a cylinder
(B) frustum of a cone and a cylinder
(C) a hemisphere and a cylinder
(D) two cylinders.
Answer: (A)
Explanation: The shape of a sharpened pencil is:
2. During conversion of a solid from one shape to another, the volume of
the new shape will
(A) increase
(B) decrease
(C) remain unaltered
(D) be doubled
Answer: (C)
Explanation: During conversion of one solid shape to another, the
volume of the new shape will remain unaltered
MCQ type:

21. 3. A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere
of diameter
(A) r cm
(B) 2r cm
(C) h cm
(D) 2h cm
Answer: (B)
Explanation: Because the sphere is enclosed inside the cylinder, therefore the
diameter of sphere is equal to the diameter of cylinder which is 2r cm
4. If two solid hemispheres of same base radii r, are joined together along their bases,
then curved surface area of this new solid is
(A) 4πr2
(B) 6πr2
(C) 3πr2
(D) 8πr2
Answer: (A)
Explanation: Because curved surface area of a hemisphere is and here we join two
solid hemispheres along their bases of radii r, from which we get a solid sphere.
Hence the curved surface area of new solid = 2πr2 + 2πr2 = 4πr2

22. 5. A solid cylinder of radius r and height h is placed over other cylinder of same
height and radius. The total surface area of the shape so formed is
(A) 4πrh + 4πr2
(B) 4πrh − 4πr2
(C) 4πrh + 2πr2
(D) 4πrh − 2πr2
Answer: (C)
Explanation: Since the total surface area of cylinder of radius r and height
h = 2πrh + 2πr2.
When one cylinder is placed over the other cylinder of same height and radius,
Then height of new cylinder = 2h
And radius of the new cylinder = r
Therefore total surface area of new cylinder
= 2πr (2h) + 2πr2
= 4πrh + 2πr2

23. 6.A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two
hemispheres stuck to each of its ends. The length of entire capsule is 2 cm.
The capacity of the capsule is
(A) 0.36 cm3
(B) 0.35 cm3
(C) 0.34 cm3
(D) 0.33 cm3
Answer: (A)
Explanation:
Since diameter of the cylinder = diameter of the hemisphere = 0.5cm
Radius of cylinder r = radius of hemisphere r = 0.5/2 = 0.25 cm
Observe the figure,

24. 7.Twelve solid spheres of the same size are made by melting a solid metallic
cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere
is
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 6 cm
Answer: (C)
Explanation:
Therefore diameter of each solid sphere = 2cm

25. 8.Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is:
(A) 3 : 4
(B) 4 : 3
(C) 9 : 16
(D) 16 : 9
Answer: (D)
Explanation: According to question,
Therefore ratio of surface area is:

26. THANK YOU
References:
1 NCERT Text book.
2. Google source.