# 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 Ã— (lb + bh + hl).
• The total surface area of a cube is given by 6 Ã— (side)2.
• The lateral surface area of a cuboidÂ is given by 2(length + breadth) Ã— height.
• Similarly, the lateral surface area of a cube of side “a” is equal to 4 Ã— (side)2.

### Lateral Area for Cylinder

• The Curved or lateral Surface Area of a Cylinder is given by 2 Ã— Ï€ Ã— r Ã— h where, r = base radius, and h = height of the cylinder.
• The total surface area of a Cylinder is given by 2Ï€r Ã— (r + h).

### Lateral Area for Cone

• The Curved Surface Area of a Cone (lateral) = Ï€ Ã— r Ã— l where, r = base radius, and l = slant height.
• The Slant height (l) =
$$\begin{array}{l}\sqrt{r^{2}+h^{2}}\end{array}$$
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
$$\begin{array}{l}= \pi rl + \pi r^{2} = \pi r(l + r)\end{array}$$

### Lateral Area for Sphere

• The lateral surface area of a sphere is given by
$$\begin{array}{l}4\pi r^{2}\end{array}$$
where r is the radius of the sphere.
• Hence, the Curved Surface Area (CSA) of a Hemisphere is given by
$$\begin{array}{l}2\pi r^{2}\end{array}$$
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 3Ï€r2.

Volume Formulas For Cube, Cuboid, Cylinder, Cone, Sphere

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