Mensuration Formulae - Part 2

Mensuration Formulas for 3D Figures

8. Mensuration Formulas for CUBOID

In the following formulae, l = length, b = breadth and h = height

Total surface area of cuboid = 2 (lb + bh + lh)

Length of diagonal of cuboid= √(l²+b²+h²)

Volume of cuboid = l × b × h

9. Mensuration Formulas for CUBE

In the following formulae, a = side of a cube

Volume of cube = a³

Total surface area of cube = 6a²

Length of Leading Diagonal of Cube = a√3

10. Mensuration Formulas for CONE

In the following formulae, r = radius of base, l = slant height of cone and h = height of the cone (perpendicular to base)

Slant height of a cone = l =√(h²+r² )

Curved surface area of a cone = C = π × r × l

Total surface area of a cone = π × r × (r + l)

Volume of right circular cone =1/3 πr²h

11. Mensuration Formulas for CYLINDER

In the following formulae, r = radius of base, h = height of cylinder

Curved surface area of a cylinder = 2πrh

Total surface area of a cylinder = 2πr(r + h)

Volume of a cylinder = πr²h

12. Mensuration Formulas for SPHERE

In the following formulae, r = radius of sphere, d = diameter of sphere

Surface area of a sphere = 4πr² = πd²

Volume of a sphere = (4/3) πr³ = (1/6)πd³

13. Mensuration Formulas for HEMISPHERE

In the following formulae, r = radius of sphere

Volume of a hemisphere =(2/3)πr³

Curved surface area of a hemisphere = 2πr²

Total surface area of a hemisphere = 3πr²

14. Mensuration Formulas for HOLLOW CYLINDER

Hollow cylinder made by cutting a smaller cylinder of same height and orientation out of a bigger cylinder.

Volume of hollow cylinder = πh(R²– r²)
(Where, R = radius of cylinder, r = radius of cavity, h = height of cylinder)

15. Mensuration Formulas for FRUSTUM OF A RIGHT CIRCULAR CONE

Frustum is created when a plane cuts a cone parallel to its base.
In the following formulae, R = radius of the base of the frustum, r = radius of the top of the frustum,
h = height of the frustum, l = slant height of the frustum

If a cone is cut by a plane parallel to the base of the cone, the lower part is called the frustum of the cone.

Slant height of the frustum =l=√(h²+(R-r)²)

Curved surface area of frustum = π(R + r)l

Total surface area of frustum = π(R + r)l + π(R² + r²)

Volume of the frustum=(1/3)πh(R²+r²+Rr)

16. Mensuration Formulas for PRISM

Prism consists of two polygonal bases which are parallel to each other.

These bases are joined by lateral faces, which are perpendicular to the polygonal bases.

The number of lateral faces is equal to the number of sides in the polygonal base. Thus, the base of a prism could be of various shapes, namely, triangular, quadrangular, pentagonal etc.

Volume of prism = Base area × height

Lateral surface area of prism = perimeter of base × height

Total surface area of prism = Lateral surface area + (2 × base area)

17. Mensuration Formula for PYRAMID

Pyramid consists of a polygonal base and triangles at its sides. These triangles are called faces.

The base could be of any shape, whereas the faces are generally isosceles triangles.

All these triangular faces meet in a single point called the apex.

Total surface area of pyramid = base area + (number of sides × ½ × slant height × base length)

Volume of pyramid = (1/3) × base area × height