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# 06 - Let's Recap - Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

## Class 10 : 06 - Let's Recap - Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

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SURFACE AREAS AND VOLUMES

Solid Figures: The objects which occupy space
width, depth and height.) are called solids. The
Example: Sphere, cone, cube,
Surface Area: The sum of the areas of the plane figures making up the boundary of a solid
figure is called its surface area

Volume: The measure of part of space occupied by a solid is called its

Lateral Surface Area: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of
i.e. Lateral area = Surface area

Cuboid: A cuboid is a box-shaped solid object
angles. All of its faces are rectangles.
• Lateral Surface Area
• Total Surface Area =
• Volume of cuboid =
Where, l = length
h = height

Cube: If the faces of a rectangular parallelepiped be squares, then it is called
• Lateral Surface Area =
• Total Surface Area =
• Volume of cube =
Where, a = side.

Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its
sides is called a right circular cylinder.
• Curved Surface Area =
• Total Surface Area =
• Volume = r
2
p
h = height

SURFACE AREAS AND VOLUMES
The objects which occupy space (i.e. they are 3 – dimensional figures having
are called solids. The solid figures are derived from the plane figures.
, cylinder, rectangular prism, etc.

The sum of the areas of the plane figures making up the boundary of a solid
surface area.
: The measure of part of space occupied by a solid is called its volume
: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of the top and the bottom.
Lateral area = Surface area – Area of two ends
shaped solid object. It has six flat sides and all the angles are right
ll of its faces are rectangles.
Lateral Surface Area = h b l ) ( 2 +
Total Surface Area = ) ( 2 hl bh lb + +
Volume of cuboid = h b l × ×

If the faces of a rectangular parallelepiped be squares, then it is called
Lateral Surface Area =
2
4a
Total Surface Area =
2
6a
Volume of cube =
3
) (a

A solid obtained by revolving a rectangular lamina about one of its
called a right circular cylinder.
Curved Surface Area = rh p 2
Total Surface Area = ) ( 2 h r r + p
h
2

, r = radius of circular base.

dimensional figures having
are derived from the plane figures.
The sum of the areas of the plane figures making up the boundary of a solid
volume.
: Lateral surface area is the area of all the sides of an object where we
It has six flat sides and all the angles are right

If the faces of a rectangular parallelepiped be squares, then it is called cube.
A solid obtained by revolving a rectangular lamina about one of its
Page 2

SURFACE AREAS AND VOLUMES

Solid Figures: The objects which occupy space
width, depth and height.) are called solids. The
Example: Sphere, cone, cube,
Surface Area: The sum of the areas of the plane figures making up the boundary of a solid
figure is called its surface area

Volume: The measure of part of space occupied by a solid is called its

Lateral Surface Area: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of
i.e. Lateral area = Surface area

Cuboid: A cuboid is a box-shaped solid object
angles. All of its faces are rectangles.
• Lateral Surface Area
• Total Surface Area =
• Volume of cuboid =
Where, l = length
h = height

Cube: If the faces of a rectangular parallelepiped be squares, then it is called
• Lateral Surface Area =
• Total Surface Area =
• Volume of cube =
Where, a = side.

Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its
sides is called a right circular cylinder.
• Curved Surface Area =
• Total Surface Area =
• Volume = r
2
p
h = height

SURFACE AREAS AND VOLUMES
The objects which occupy space (i.e. they are 3 – dimensional figures having
are called solids. The solid figures are derived from the plane figures.
, cylinder, rectangular prism, etc.

The sum of the areas of the plane figures making up the boundary of a solid
surface area.
: The measure of part of space occupied by a solid is called its volume
: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of the top and the bottom.
Lateral area = Surface area – Area of two ends
shaped solid object. It has six flat sides and all the angles are right
ll of its faces are rectangles.
Lateral Surface Area = h b l ) ( 2 +
Total Surface Area = ) ( 2 hl bh lb + +
Volume of cuboid = h b l × ×

If the faces of a rectangular parallelepiped be squares, then it is called
Lateral Surface Area =
2
4a
Total Surface Area =
2
6a
Volume of cube =
3
) (a

A solid obtained by revolving a rectangular lamina about one of its
called a right circular cylinder.
Curved Surface Area = rh p 2
Total Surface Area = ) ( 2 h r r + p
h
2

, r = radius of circular base.

dimensional figures having
are derived from the plane figures.
The sum of the areas of the plane figures making up the boundary of a solid
volume.
: Lateral surface area is the area of all the sides of an object where we
It has six flat sides and all the angles are right

If the faces of a rectangular parallelepiped be squares, then it is called cube.
A solid obtained by revolving a rectangular lamina about one of its

SURFACE AREAS AND VOLUME

Right Circular Cone: A right circular cone is a solid generated by the revolution of a right
angled triangle about one of its side
• Curved Surface Area
• Total Surface Area =
• Volume =
3
1
p
Where, r = radius of base.
h = height
l = slant height

Sphere: A sphere is a solid generated by the revolution of a semi

• Curved Surface Area =
• Total Surface Area =
• Volume =
3
4
p

Spherical shell: A spherical shell is a generalization of an annulus to three dimensions
• Volume =
3
4
p
Where,
1
r and
2
r are its
• Total Surface Area

Hemisphere: A plane passing through the centre
each called a hemisphere.
• Curved Surface Area =
• Total Surface Area =
• Volume =
3
2
p

SURFACE AREAS AND VOLUMES
right circular cone is a solid generated by the revolution of a right
angled triangle about one of its side containing the right angle as axis.

Curved Surface Area = rl p
=
2 2
h r r + p
Total Surface Area = ) ( r l r + p
h r
2
p
, r = radius of base.

l = slant height
sphere is a solid generated by the revolution of a semi-circle about its diameter.
Curved Surface Area =
2
4 r p
Total Surface Area =
2
4 r p
3
r p
A spherical shell is a generalization of an annulus to three dimensions
) (
3
2
3
1
r r -
are its external and internal radii respectively.
Total Surface Area = ) ( 4
2
2
2
1
r r + p
A plane passing through the centre of a sphere cuts the sphere in two equal parts

Curved Surface Area =
2
2 r p
Total Surface Area =
2
3 r p
3
r p
S
right circular cone is a solid generated by the revolution of a right

A spherical shell is a generalization of an annulus to three dimensions.
respectively.
cuts the sphere in two equal parts

Page 3

SURFACE AREAS AND VOLUMES

Solid Figures: The objects which occupy space
width, depth and height.) are called solids. The
Example: Sphere, cone, cube,
Surface Area: The sum of the areas of the plane figures making up the boundary of a solid
figure is called its surface area

Volume: The measure of part of space occupied by a solid is called its

Lateral Surface Area: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of
i.e. Lateral area = Surface area

Cuboid: A cuboid is a box-shaped solid object
angles. All of its faces are rectangles.
• Lateral Surface Area
• Total Surface Area =
• Volume of cuboid =
Where, l = length
h = height

Cube: If the faces of a rectangular parallelepiped be squares, then it is called
• Lateral Surface Area =
• Total Surface Area =
• Volume of cube =
Where, a = side.

Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its
sides is called a right circular cylinder.
• Curved Surface Area =
• Total Surface Area =
• Volume = r
2
p
h = height

SURFACE AREAS AND VOLUMES
The objects which occupy space (i.e. they are 3 – dimensional figures having
are called solids. The solid figures are derived from the plane figures.
, cylinder, rectangular prism, etc.

The sum of the areas of the plane figures making up the boundary of a solid
surface area.
: The measure of part of space occupied by a solid is called its volume
: Lateral surface area is the area of all the sides of an object where we
don’t have to count the areas of the top and the bottom.
Lateral area = Surface area – Area of two ends
shaped solid object. It has six flat sides and all the angles are right
ll of its faces are rectangles.
Lateral Surface Area = h b l ) ( 2 +
Total Surface Area = ) ( 2 hl bh lb + +
Volume of cuboid = h b l × ×

If the faces of a rectangular parallelepiped be squares, then it is called
Lateral Surface Area =
2
4a
Total Surface Area =
2
6a
Volume of cube =
3
) (a

A solid obtained by revolving a rectangular lamina about one of its
called a right circular cylinder.
Curved Surface Area = rh p 2
Total Surface Area = ) ( 2 h r r + p
h
2

, r = radius of circular base.

dimensional figures having
are derived from the plane figures.
The sum of the areas of the plane figures making up the boundary of a solid
volume.
: Lateral surface area is the area of all the sides of an object where we
It has six flat sides and all the angles are right

If the faces of a rectangular parallelepiped be squares, then it is called cube.
A solid obtained by revolving a rectangular lamina about one of its

SURFACE AREAS AND VOLUME

Right Circular Cone: A right circular cone is a solid generated by the revolution of a right
angled triangle about one of its side
• Curved Surface Area
• Total Surface Area =
• Volume =
3
1
p
Where, r = radius of base.
h = height
l = slant height

Sphere: A sphere is a solid generated by the revolution of a semi

• Curved Surface Area =
• Total Surface Area =
• Volume =
3
4
p

Spherical shell: A spherical shell is a generalization of an annulus to three dimensions
• Volume =
3
4
p
Where,
1
r and
2
r are its
• Total Surface Area

Hemisphere: A plane passing through the centre
each called a hemisphere.
• Curved Surface Area =
• Total Surface Area =
• Volume =
3
2
p

SURFACE AREAS AND VOLUMES
right circular cone is a solid generated by the revolution of a right
angled triangle about one of its side containing the right angle as axis.

Curved Surface Area = rl p
=
2 2
h r r + p
Total Surface Area = ) ( r l r + p
h r
2
p
, r = radius of base.

l = slant height
sphere is a solid generated by the revolution of a semi-circle about its diameter.
Curved Surface Area =
2
4 r p
Total Surface Area =
2
4 r p
3
r p
A spherical shell is a generalization of an annulus to three dimensions
) (
3
2
3
1
r r -
are its external and internal radii respectively.
Total Surface Area = ) ( 4
2
2
2
1
r r + p
A plane passing through the centre of a sphere cuts the sphere in two equal parts

Curved Surface Area =
2
2 r p
Total Surface Area =
2
3 r p
3
r p
S
right circular cone is a solid generated by the revolution of a right

A spherical shell is a generalization of an annulus to three dimensions.
respectively.
cuts the sphere in two equal parts

SURFACE AREAS AND VOLUME

Frustum of a Cone: If a cone is cut by a plane parallel to the base of the cone, then the portion
between the plane and base is called the
• Curved Surface Area
Where,
1
2
(r h l + =
• Total Surface Area =
• Volume =
3
1
h p
Where, h    = vertical height
l   = slant height
=
2 1
,r r radii of the two bases.

Surface Area of a Combination of solid:
the curved surface areas of each of the individual parts.
Example:

TSA of new solid = CSA of one hemisphere + CSA of cylinder +
Where, TSA= Total Surface Area
and CSA=Curved Surface Area

Volume of a Combination of Solids:
two basics solids will actually be the sum of the volumes of the constituents.

SURFACE AREAS AND VOLUME
If a cone is cut by a plane parallel to the base of the cone, then the portion
base is called the frustum of a cone.
Curved Surface Area = ) (
2 1
r r l + p
2
2 1
) r -
Total Surface Area = ) ( ) (
2
2
2
1 2 1
r r r r l + + + p p
) (
2 1
2
2
2
1
r r r r + +
= vertical height
= slant height
Surface Area of a Combination of solid: The total surface area of the new solid is the sum of
the curved surface areas of each of the individual parts.
of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemisphere
Where, TSA= Total Surface Area
CSA=Curved Surface Area
Volume of a Combination of Solids: The volume of combination of the solid formed by joining
will actually be the sum of the volumes of the constituents.

SURFACE AREAS AND VOLUME
If a cone is cut by a plane parallel to the base of the cone, then the portion
The total surface area of the new solid is the sum of
CSA of other hemisphere
ombination of the solid formed by joining
will actually be the sum of the volumes of the constituents.
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## Crash Course for Class 10 Maths by Let's tute

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