Chapter 13: Surface Area and Volume: Key Points and Concepts

CHAPTER 13: SURFACE AREA AND VOLUME
Topics to be covered-
➢ Surface Area of a combination of solids
➢ Volume of different solids
➢ Conversion of solid from one form to another
Key Points and Concepts:
➔ Surface Area solids

Surface area of a solid is defined as the amount of space covering the outside of a
three-dimensional shape. Surface area of commonly used solids is shown in the
table below:
Solid Shape Surface Area
Cube 𝑆𝐴 = 6 × (𝑠𝑖𝑑𝑒)
2
Cuboid 𝑆𝐴 = 2(𝑙𝑏 + 𝑏ℎ + 𝑙ℎ)

Where, l = length,
b=breadth, h=height
Cone 2
𝑆𝐴 = π𝑟 (𝑟 + 𝑙)
Where, r= radius, l = slant
height
Sphere 𝑆𝐴 = 4π𝑟
2
where r=radius
Hemisphere 𝑆𝐴 = 2π𝑟
2
where r=radius
Cylinder 𝑆𝐴 = 2π𝑟(𝑟 + ℎ)
where r=radius, h=height
➔ Surface Area of combination of Solids

Surface area of a combination of solids is calculated by dissecting the solid first and
then using formulas to find the answer. Ideally, the total curved surface area of the
combination of solids is calculated by adding the curved surfaces of the individual
solids.
For example, in the case of the combination of solid given, the solid is formed by the
combination of cylinder and hemisphere. The total surface area would be the addition of
the surface area hemisphere or cylinder.
3
Q. : The radius of a sphere (in cm) whose volume is 12p 𝑐𝑚 is ……[CBSE Standard 2020]
Q. A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the
volume of the rice. How much canvas cloth is required to just cover the heap? [CBSE 2018]
Q.Volume and surface area of a solid hemisphere are numerically equal. What is the
diameter of hemisphere? [Delhi 2017]
➔ Volume of combination of solids
The volume of the solid formed by joining two basic solids will actually be the sum of
the volumes of the constituents.
Solid Shape Volume
Cube 𝑉𝑜𝑙𝑢𝑚𝑒 = (𝑠𝑖𝑑𝑒)

3
Cuboid 𝑉𝑜𝑙𝑢𝑚𝑒 = (𝑙 . 𝑏 . ℎ )
Where, l = length,
b=breadth, h=height
Right Circular Cone 2

𝑣𝑜𝑙𝑢𝑚𝑒 = (π𝑟 (ℎ))/3
Where, r= radius, l = slant
height
Sphere 4 3
Volume = π𝑟
3
where, r=radius
Hemisphere 2 3
Volume = π𝑟
3
where r=radius
Right circular Cylinder Volume = π𝑟 (ℎ)
2
where r=radius, h=height
Q. A cone and a cylinder have the same radii but the height of the cone is 3 times that of the
cylinder. Find the ratio of their volumes. [CBSE Standard 2020]
1 3
Q. The volume of a right circular cylinder with its height equal to the radius is 25 7
𝑐𝑚 .
22
Find the height of the cylinder. [Use Π = 7
] [CBSE Standard 2020]
Q. A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the
volume of the rice. How much canvas cloth is required to just cover the heap? [CBSE 2018]
➔ Conversion of solid from one form to another

In case of the conversion of solid from one form to another, the volume of the earlier
solid is equal to the volume of the new solid.
If a solid of one shape is converted into solid (or solids) of another shape, then
❖ Volume of the solid to be converted = Total volume of the solids into which
the given solid is to be converted
❖ Number of solids of a given shape in which a given solid is to be converted
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑙𝑖𝑑 𝑡𝑜 𝑏𝑒 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑
Is equal to
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝑠𝑜𝑙𝑖𝑑
Q. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to
form a cuboid of dimensions 5.5cm × 10 cm × 3.5 cm? [CBSE 2011]
3
Q.The 4
th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water.
The water is emptied into a cylindrical vessel with an internal radius 10 cm. Find the height
of water in a cylindrical vessel. [Delhi 2017]
*** Evaluate your level of knowledge by solving this Quiz ***
THE SALIENT FEATURES OF THE NOTES PDF ARE:
1. The note pdf has been prepared chapter-wise, so that a student can prepare
the entire syllabus chronologically according to the new reduced syllabus.
2. Fast track revision- A quick recall of the chapter is gained through this pdf.
3. CBSE Examination questions acquaint the students with the pattern of
questions asked in board exams from each chapter and topic,
4. Link of the Mock test papers according to the latest blueprint specified by
CBSE. To recall your knowledge.
5. TERM II will be subjective, so learn, memorize, understand, definition and
theories from this note pdf.

Chapter 13: Surface Area and Volume: Key Points and Concepts

Uploaded by

Copyright:

Available Formats

Chapter 13: Surface Area and Volume: Key Points and Concepts

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Chapter 13: Surface Area and Volume: Key Points and Concepts

Uploaded by

Copyright:

Available Formats

CHAPTER 13: SURFACE AREA AND VOLUME

Key Points and Concepts:

➔ Surface Area solids

Solid Shape Surface Area

Cuboid 𝑆𝐴 = 2(𝑙𝑏 + 𝑏ℎ + 𝑙ℎ)

➔ Surface Area of combination of Solids

➔ Volume of combination of solids

Cube 𝑉𝑜𝑙𝑢𝑚𝑒 = (𝑠𝑖𝑑𝑒)

Right Circular Cone 2

where r=radius, h=height

➔ Conversion of solid from one form to another

You might also like