What is the Surface Area of a Dome?

The surface area of a dome refers to the total area of its curved surface. It is a portion of the surface area of a sphere. The calculation depends on the dimensions of the dome, particularly its radius and height.

Dome Surface Area Formula

For a dome with a circular base, the surface area is calculated using the following formula:

$A = 2 \pi r h$

Where:

• A is the surface area of the dome.
• r is the radius of the dome's base.
• h is the height of the dome.

Step-by-Step Example

Let’s calculate the surface area of a dome with:

• Radius (r) = 5 meters
• Height (h) = 10 meters

Using the Formula:

$\begin{aligned} A &= 2 \pi r h \\ A &= 2 \pi (5) (10) \\ A &= 100 \pi \\ A &\approx 314.16 \, \text{m}^2 \end{aligned}$

The surface area of the dome is approximately 314.16 square meters.

FAQ

What is the difference between a dome's curved surface area and total surface area?

Curved Surface Area: This refers only to the rounded, outer shell of the dome. It excludes the base.

Total Surface Area: This includes the curved surface area plus the area of the circular base, if applicable. For a complete dome, it’s the curved surface plus the flat base area:

$\text{Total Surface Area} = 2 \pi r h + \pi r^2$