Find the surface area.

sphere: area of great circle = 29.8m^2

To find the surface area of a sphere using the area of the great circle, you can use the formula:

Surface Area = 4πr^2

where π is a mathematical constant (approximately 3.14159) and r is the radius of the sphere.

Now, to find the radius from the given area of the great circle, you can rearrange the equation:

Area = πr^2

29.8m^2 = πr^2

To determine the radius, divide both sides of the equation by π:

r^2 = 29.8m^2 / π

r^2 ≈ 9.4834

Taking the square root of both sides, we can find the value of r:

r ≈ √9.4834

r ≈ 3.08m

Now that we have the radius, we can substitute it back into the surface area formula:

Surface Area = 4π(3.08m)^2

Surface Area ≈ 4 * 3.14159 * (3.08m)^2

Surface Area ≈ 4 * 3.14159 * 9.4864m^2

Surface Area ≈ 119.209m^2

Therefore, the surface area of the sphere is approximately 119.209 square meters.

To find the surface area of a sphere, you need to know the area of its great circle.

The formula for the surface area of a sphere is:

Surface Area = 4πr²

Where "r" is the radius of the sphere.

Since the given area of the great circle is 29.8 m², we can find the radius using the formula for the area of a circle:

Area of a Circle = πr²

Rearranging the formula, we have:

r = √(Area of Great Circle / π)

Substituting the given area of the great circle, we get:

r = √(29.8 m² / π)

Now, we can use the radius to calculate the surface area of the sphere:

Surface Area = 4π(√(29.8 m² / π))²

Simplifying further, we have:

Surface Area = 4π(29.8 m² / π)

Canceling out the π terms, we get:

Surface Area = 4 * 29.8 m²

Finally, evaluating the expression, the surface area of the sphere is:

Surface Area = 119.2 m²

since the circle has area πr^2, and the sphere has surface area 4πr^2, what do you think?