Ncert Solutions for Class 9 Maths Chapter 13 pdf covers the topic of surface areas and volumes class 9 and the formulas to calculate the areas and volumes of Square, Rectangle, Triangle, Circle. To get more in-depth knowledge on surface areas and volumes class 9 refer to  ncert solutions for class 9 maths chapter 13 pdf download

Area

The space occupied by a two-dimensional flat surface. It is measure in square units.

Generally, Area can be of two types

(i) Total Surface Area

(ii) Curved Surface Area

Total Surface Area

Total surface area refers to area including the base(s) and the curved part.

 Curved surface area (lateral surface area)

Refers to area of only the curved part excluding it’s base(s).

Volume

The amount of space, measured in cubic units, that an object or substance occupies.

Surface area and volume all formulas

The Surface area and volume all formulas are given below:

Areas

square = a²  

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b₁+ b₂)

circle = pir ²

ellipse = pir₁ r₂

• triangle = (1/2) b h
• equilateral triangle = (1/4)(3) a²
• triangle given SAS = (1/2) a b sin C
• triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron’s formula)
• regular polygon = (1/2) n sin(360°/n) S²
  when n = # of sides and S = length from center to a corner

 Volumes

cube = a³

rectangular prism = a b c

irregular prism = bh

cylinder = bh =  r² h

pyramid = (1/3) bh

Cone = (1/3) bh = 1/3  r² h

sphere = (4/3) r³

ellipsoid = (4/3) pir₁ r₂ r₃

Surface Areas

cube = 6 a²

prism:
(lateral area) = perimeter(b) L
(total area) = perimeter(b) L + 2b

sphere = 4 r²