Question

What is the surface area of a sphere with an area of a great circle of 814.3

Answer 1

3257.94 square units.

Explanation:

To find the surface area of a sphere with the area of a great circle given, we can use the formula:

Surface Area = 4πr^2

Here, r represents the radius of the sphere.

Since the area of a great circle is equal to πr^2, we can determine the radius using the given area. Let's solve for r:

πr^2 = 814.3

Divide both sides of the equation by π:

r^2 = 814.3 / π

r^2 ≈ 259.65

Now, take the square root of both sides to find the radius:

r ≈ √259.65

r ≈ 16.10 (rounded to two decimal places)

Now that we have the radius, we can calculate the surface area of the sphere:

Surface Area = 4πr^2

Surface Area = 4π(16.10)^2

Surface Area ≈ 4π(259.21)

Surface Area ≈ 1036.84π

Answer 2

The formula for finding the surface area of a sphere is given as;`Surface area of sphere = 4πr²`, where r is the radius of the sphere.We are given that the area of a great circle is 814.3.Therefore, the circumference of the great circle can be calculated as;`Circumference = πd`, where d is the diameter of the sphere.Since the great circle is a cross-section of the sphere, we can say that it is equal to the circumference of the sphere.`πd = 814.3`We can rearrange this formula to find the diameter;`d = 814.3/π`We can then use the diameter to find the radius of the sphere;`r = d/2`Now, we can substitute the value of r in the formula of the surface area of the sphere;`Surface area of sphere = 4πr²`= 4 x π x (d/2)²`= 4 x π x (814.3/2π)²`= 166271.2`Therefore, the surface area of the sphere is approximately equal to 166271.2 square units.