Find the surface area of a hemisphere with a radius 20m. Leave your answer in terms of pi

1 answer

The surface area \( A \) of a hemisphere is calculated using the formula:

\[ A = 2\pi r^2 + \pi r^2 \]

where:

  • The term \( 2\pi r^2 \) is the curved surface area,
  • The term \( \pi r^2 \) is the area of the circular base.

However, if we only want the curved surface area of the hemisphere, we use:

\[ A = 2\pi r^2 \]

Let's substitute the radius \( r = 20 \) meters into the formula for the curved surface area:

\[ A = 2\pi (20)^2 \] \[ A = 2\pi (400) \] \[ A = 800\pi \]

If considering the total surface area including the base:

\[ A_{\text{total}} = 2\pi r^2 + \pi r^2 = 3\pi r^2 \] \[ A_{\text{total}} = 3\pi (20)^2 \] \[ A_{\text{total}} = 3\pi (400) \] \[ A_{\text{total}} = 1200\pi \]

Thus, the surface area of the hemisphere (including the base) is \( 1200\pi \) square meters, while the curved surface area is \( 800\pi \) square meters.

So, to summarize:

  • Curved surface area: \( 800\pi \) m²
  • Total surface area (including base): \( 1200\pi \) m²