 # 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 3πr2.

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

• 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.