NCERT Notes for Class 10 Maths Chapter 13 Surface Areas and Volumes
Class 10 Maths Chapter 13 Surface Areas and Volumes Notes
Chapter Name  Surface Areas and Volumes Notes 
Class  CBSE Class 10 
Textbook Name  Mathematics Class 10 
Related Readings 

Surface area: Surface area of an object is the measure of the total area that the surface of an object occupies.
Volume: Volume of an object is the measure of space occupied by the object.
Basic Solids: In standard X, we have studied the surface area and volume of solids. Here we will study more about them.
Surface Area and Volume of Cuboid
h is the height
(ii) Area of four walls of cuboid
= 2(l + b) × h
= [Perimeter of floor × Height] sq. unit
(iii) Surface area of cuboid without roof or lid
= lb + 2[bh + lh] sq. unit
(iv) Volume of cuboid = l × b × h unit
(v) Diagonal of cuboid or length of longest rod kept = unit
Surface Area and Volume of Cube
Let each edge of a cube be of length a unit. Then,
(i) Surface area of cube = 6 side^{2} = 6a^{2} unit
(ii) Surface area of four walls of cube = 4 side^{2}= 4a^{2} sq. unit
(iii) Surface area of a cube without lid (or rod) of a cube
= 5a^{2} sq. unit.
(iv) Length of longest diagonal (or rod) of a cube
= unit
(v) Volume of cube = a^{3} unit
Surface Area and Volume of Cylinder
(i) Curved surface area of cylinder = 2πr × h
= Perimeter of base × height sq. unit
(ii) Total surface area of cylinder
= CSA + Area of 2 circular ends of cylinder
= 2πrh + 2πr^{2} = 2πr (r + h)
(iv) Volume of material in hollow pipe = Exterior volume – Interior volume
= πR^{2}h – πr^{2}h = πh [R^{2} – r^{2}]
(v) Total surface area of hollow cylinder
= CSA of outer and inner cylinder + 2(area of base ring)
= 2πRh + 2πrh + 2(πR^{2} – πr^{2})
= 2π(R + r)h + 2π(R^{2} – r^{2}) = 2π(R + r) (h + R – r)
Note:
 Two ends of cylinder are circles having each area = πr^{2}
 Mass of cylinder = Volume of cylinder × Density
⇒ M = V × ρ
Surface Area and Volume of Cone
h = OA = height of cone
r = OB = radius of cone
l = AB = slant height of cone
(i) Slant height of cone = l = units
(ii) Curved surface area of cone or lateral surface area of cone = πrl sq. unit
(iii) Total surface area of cone = CSA + Area of circular base
= πrl + πr^{2} – πr(r + l) sq. unit
(iv) Volume of cone = 13 πr^{2}h cu. unit
Surface Area and Volume of Sphere
 Surface area of sphere = 4πr^{2}unit
 Volume of sphere = 4/3 cu.unit
Surface Area and Volume of Hemisphere
 Curved surface area of hemisphere = 4πr^{2}sq unit
 Volume of hemisphere =2/3 πr^{2} cu unit
 Total surface area of hemisphere = 2πr^{2 }+ πr^{2} = 3πr^{2} unit
(i) Total surface area of spherical shell = 4πR^{2} + 4πr^{2}
= 4πr(R^{2} + r^{2}) sq. unit
(ii) Volume of spherical shell = cu . unit
Surface Area and Volume of Shapes of Frustum
(i) Slant height of frustum = unit
(ii) Curved surface area of frustum = π(R + r)l sq. unit
(iii) Total surface area of frustum of cone
= πl (R + r) + πR^{2} + πr^{2} sq. unit
(iv) Volume of frustum of cone = sq. unit
Volume of Combination Solids
The volume of the solid formed by joining two basic solids will actually be the sum of the volumes of the two basic solids.
Conversion of Solid from One Shape to Another
If we melt the candle in the shape of cylinder and pour it into a conical vessel, then it changes into the conical shape. Thus, volume of cylindrical candle = Volume of conical solid.