what is the approximate surface area of the sphere?
A sphere labeled upper C is 37.68 km. c=circumference
If the circumference of a sphere is given as 37.68 km, we can use that information to find the radius of the sphere.
The formula for the circumference of a sphere is given by:
C = 2πr
where C is the circumference and r is the radius.
Rearranging the formula, we get:
r = C / 2π
Substituting the given value of circumference, we get:
r = 37.68 km / 2π
r ≈ 6.0 km (rounded to one decimal place)
Now that we know the radius of the sphere, we can use the formula for the surface area of a sphere, which is:
A = 4πr^2
Substituting the value of r, we get:
A = 4π(6.0 km)^2
A ≈ 452.4 km^2 (rounded to two decimal places)
Therefore, the approximate surface area of the sphere is 452.4 km^2.
Note: This answer is different from the previous answer because we assumed that the circumference given was for the equator of the sphere, whereas the previous answer assumed it was the circumference of the sphere itself. Depending on the context, either assumption may be valid.
To find the approximate surface area of a sphere, you need to use the formula:
Surface Area = 4πr^2
In the given information, "c" represents the circumference of the sphere, and it is mentioned to be 37.68 km. The formula for the circumference of a sphere is:
Circumference = 2πr
From this, we can calculate the radius of the sphere. Rearranging the formula, we get:
r = Circumference / (2π)
Plugging in the given value for the circumference (37.68 km):
r ≈ 37.68 km / (2π)
Now that we have the radius, we can substitute it into the formula for the surface area:
Surface Area ≈ 4π(37.68 km / (2π))^2
Simplifying further:
Surface Area ≈ 4π(37.68 km / 6.28)^2
Surface Area ≈ 4π(6 km)^2
Surface Area ≈ 4π(36 km^2)
Surface Area ≈ 144π km^2
So, the approximate surface area of the sphere is 144π square kilometers.
The circumference (C) of a sphere is given by the formula C = 2πr, where r is the radius of the sphere. We can rearrange the formula to solve for the radius, r = C / (2π).
Given that C = 37.68 km, we can calculate the radius:
r = 37.68 km / (2π)
r ≈ 37.68 km / (2 * 3.1416)
r ≈ 2.995 km
Now that we have the radius, we can calculate the surface area (A) of the sphere using the formula A = 4πr²:
A ≈ 4 * 3.1416 * (2.995 km)²
A ≈ 4 * 3.1416 * 8.970025 km²
A ≈ 12.5664 * 8.970025 km²
A ≈ 112.744 km²
So, the approximate surface area of the sphere is 112.744 km².