Lateral Area Formula

The lateral area of a figure is the area of the non-base faces only. In this article, the lateral surface area of different figures including cuboid, cube, cylinder, cone, and sphere.

Formulas for Lateral Surface Area

  • Lateral Area for Cuboid and Cube

The Total surface area of a cuboid is given by 2 (length . breadth + breadth . height + height . length) = 2 × (lb + bh + hl). The total surface area of a cube is given by 6 × (side)2.

The lateral surface area of a cuboid is given by 2(length + breadth) × height. Similarly, the lateral surface area of a cube of side “a” is equal to 4 × (side)2.

  • Lateral Area for Cylinder

The Curved or lateral Surface Area of a Cylinder is given by 2 × π × r × h where, r = base radius, and h = height of the cylinder. The total surface area of a Cylinder is given by 2πr × (r + h).

  • Lateral Area for Cone

The Curved Surface Area of a Cone (lateral) = π × r × l where, r = base radius, and l = slant height. The Slant height (l) = \(\sqrt{r^{2}+h^{2}}\) where, h = height of cone. If the base of the cone is to be closed, then the total Surface Area of a Cone is given by \(= \pi rl + \pi r_{2} = \pi r(l + r)\)

  • Lateral Area for Sphere

The lateral surface area of a sphere is given by \(4\pi r^{2}\) where r is the radius of the sphere. Hence, the Curved Surface Area (CSA) of a Hemisphere is given by \(2\pi r^{2}\) where r is the radius of the sphere of which the hemisphere is a part. The total surface area (TSA) of a Hemisphere is given by 3π.

The Volume of a Cuboid is given by (area of base × height) i.e. height × (length × breadth). The volume of a Cube is given by \(edge^{3}\). The Volume of a Cylinder is given by \(\pi r^{2} h\) where r = radius of base and h = given height of the cylinder. The Volume of a Cone is given by \(\frac{1}{3}\pi r^{2}h\) where r = base radius and h = height of the cone. The Volume of a Sphere is given by \(\frac{4}{3}\pi r^{3}\) where r is the radius of the sphere.


Practise This Question

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is  [IIT 1985]