Lateral Area Formula For Three Dimensional Shapes - Byju's

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) = \(\begin{array}{l}\sqrt{r^{2}+h^{2}}\end{array} \) 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 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 \(\begin{array}{l}edge^{3}\end{array} \).
• 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.

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