Important formulas to be remember before you go to class 10th

Class 9 Maths Formulae for Circle

A circle is a closed geometrical figure. All points on the boundary of a circle are equidistant from a fixed point inside the circle (called the center).

1. Area of a circle (of radius r) = π × r2
2. The diameter of the circle, d = 2 × r
3. Circumference of the circle = 2 × π × r
4. Sector angle of the circle, θ = (180 × l ) / (π × r )
5. Area of the sector = (θ/2) × r2; where θ is the angle between the two radii
6. Area of the circular ring = π × (R2 – r2); where R – radius of the outer circle and r – radius of the inner circle

Class 9 Maths Heron’s Formula

Heron’s Formula is used to calculate the area of a triangle whose all three sides are known. Let’s suppose the length of three sides are a, b and c.

• Step 1 – Calculate the semi-perimeter, s=a+b+c2$s=(\frac{a+b+\mathrm{c)/}}{2}$

• Step 2 – Area of the triangle,
  
  

Class 9 Maths Formulae for Surface Areas & Volumes

Here, LSA stands for Lateral/Curved Surface Area and TSA stands for Total Surface Area

Cuboid

LSA: 2h(l + b)
TSA: 2(lb + bh + hl)
Volume: l × b × h

l = length,
b = breadth,
h = height

Cube

LSA: 4a2
TSA: 6a2
Volume: a3

a = sides of a cube

Right Circular Cylinder

LSA: 2(π × r × h)
TSA: 2πr (r + h)
Volume: π × r2 × h

r = radius,
h = height

Right Circular Cone

LSA: πrl
TSA: π × r × (r + l)
Volume: ⅓ × (πr2h)

r = radius,
l = slant height,
h = height

Hemisphere

LSA: 2 × π × r2
TSA: 3 × π × r2
Volume: ⅔ × (πr3)

r = radius

Sphere

LSA: 4 × π × r2
TSA: 4 × π × r2
Volume: 4/3 × (πr3)

r = radius

Right Pyramid

LSA: ½ × p × l
TSA: LSA + Area of the base
Volume: ⅓ × Area of the base × h

p = perimeter of the base,
l = slant height, h = height

Prism

LSA: p × h
TSA: LSA × 2B
Volume: B × h

p = perimeter of the base,
B = area of base, h = height