Question

A scientist wants to find the radius, in meters, of this hemispherical dome. She finds that the surface area of the entire sphere containing the dome is 520 square meters. Which equation could she use to find the dome's radius?

Answer 1

The surface area of the entire sphere containing the dome can be expressed in terms of the radius of the sphere, which is also the radius of the dome.

The surface area of a sphere with radius r is given by the formula:

4πr^2

Since the surface area of the entire sphere containing the dome is 520 square meters, we can set up the following equation:

4πr^2 = 520

To find the radius of the dome, we can solve for r by dividing both sides of the equation by 4π and then taking the square root:

r = sqrt(520 / 4π)

Simplifying this expression, we get:

r = sqrt(130 / π)

Therefore, the equation the scientist can use to find the dome's radius is:

r = sqrt(130 / π)