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