Surface Areas and Volumes Class 10th Notes - Free NCERT Class 10 Maths Chapter 13 Notes - Download PDF

NCERT Class 10 Maths chapter 13 notes based on Surface, areas, and volumes, in which all the solid shapes are included and how to calculate the areas, volumes, or surface areas, total surface areas of curved shape can be easily evaluated. The chapter Surface, areas, and volumes Class 10 Notes also include combined shapes formulas.

Introductory Part may include: The NCERT Class 10 chapter 13 notes Properties of Surface, areas, and volumes are the highlighting key feature of Surface, areas and volumes 10 notes. CBSE Class 10 Maths chapter 13 notes also cover the basic formulae in the chapter. CBSE Class 10 Maths chapter 13 notes contain systematic explanations of topics using examples and exercises. All these topics can be downloaded from Class 10 Maths chapter 13 notes pdf download.

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NCERT Class 10 Chapter 13 Notes-

Surface, Areas, and Volumes Class 10 Notes- Topic 1:

Surface area: Surface area can be defined as the measurement of the total area that has been occupied by the object.

Volume: Volume is defined as the measurement of space that is occupied by the object.

Surface, Areas, and Volumes Class 10 Notes- Topic 2:

Basic solid shapes and their respective formula will be discussed in this chapter.

Cuboid :

The surface area of a cuboid with the roof.

The surface area of the cuboid is equal to 2(lb +bh +hl) sq. unit.

Here, l denotes the length, b denotes the breadth, h denotes the height.

Area of Cuboid:

Area of cuboid covering four walls= [Perimeter length is multiplied by height] sq. unit.

= 2(l+ b) h

Surface area of cuboid with no roof:

Surface area with no roof =lb+2[bh +hl]

Volume of cuboid:

Volume = l×b×h unit.

Cube :

In this let us consider that each edge of length is to be taken as “a” unit.

Surface area:

Area of a cube that covers all the side = 6side2

= 6a²

Area of covered by all the four walls = 4side2

= 4a² sq. units.

The surface area of a cube with no lid:

Area of a cube with no roof or lid=5 side2

= 5a² sq. unit

Cylinder :

Surface area:

Surface area is taken as curved = base perimeter× height

= 2rπ×h

Total surface area can be calculated as the sum of curved surface area, and the area of two circular ends of the cylinder

Total surface area = 2rπh×2πr²

= 2rπ(r+h)

Volume:

Cylinder’s Volume = πr²h

The other volume which is a material present in a hollow pipe

= External volume- Internal Volume

=πR²h-πr²h

=πh[R²-r²]

The surface area of Hollow cylinder:

The total surface area of the hollow cylinder can be calculated as the curved surface area of the outer cylinder and inner cylinder with the addition of two base rings.

2Rπh+ 2rπh+ 2[πR²-πr²]

Cone :

Slant height or length:

Slant height (l²) = (r²+h²) units.

h= height of the cone

r =radius of the cone

l = slant height of the cone

Surface area:

Surface area covered by all sides or lateral surface area= rπl sq unit.

Total surface area is to be calculated as the sum of curved surface area and area of base which is circular.

[rπl+ πr²] sq. unit

Volume:

Cone’s Volume = πr²h/3 cubic unit.

Sphere :

Surface area:

The surface area of the sphere can be calculated as 4πr².

Volume:

Sphere’s Volume = 4πr³/3 cubic unit.

Hemisphere :

Surface area:

The surface area which is curved = 2πr²

Total surface area is calculated as = 2πr²+ πr²= 3πr²

Volume:

Hemisphere’s Volume = 2πr³/3 cubic unit.

Spherical Shell :

Surface area:

Taking r₂=r and r₁=R

Total surface area can be calculated as = 4πr²+4πR².

= 4π(r²+R²) sq. unit.

Volume:

Spherical shell’s volume = 4π(R³-r³)/3 cubic unit.

Shapes of Frustum :

Surface area:

Curved surface area can be calculated using = πrl(R+r)

Here, l is the slant height which is calculated using the slant height of frustum formulae.

The total surface area of the frustum of the cone can be calculated using = πrl(R+r)+ πr²+πR² sq. unit.

Slant height:

Slant height(l²) = (R-r)²+h²

Volume:

Frustum Cone’s volume = πh(r²+R²+Rr)/3 sq. unit.

Surface, Areas, and Volumes Class 10 Notes- Topic 3:

Calculation of volume of a combination of solids can be done in accordance with the joining of two basic solids and then evaluate the sum of volumes of two.

Conversion of solids:

Conversion of shapes from one state to another can be possible by melting one solid shape and joining this with another.

Significance of NCERT Class 10 Maths Chapter 13 Notes

Surfaces, areas, and volumes Class 10 notes, will help to understand the formulas, statements, rules in detail. Also, this NCERT Class 10 Maths chapter 13 contains previous year’s questions and NCERT TextBook pdf. Surfaces, areas, and volumes Class 10 notes contain FAQ or frequently asked questions along with a topic-wise explanation. The Surfaces, areas, and volumes of Class 10 notes can be helpful in offline mode as well after downloading the notes.

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