Answer:
To find the volume of a sphere with a surface area of 1,000 square centimeters, we need to use the formula for the surface area of a sphere and solve for the radius first.
The formula for the surface area of a sphere is:
Surface Area = 4πr²
Given that the surface area is 1,000 square centimeters, we can solve for the radius (r) using the formula:
1,000 = 4πr²
Divide both sides of the equation by 4π:
r² = 1,000 / (4π)
r² = 250 / π
Now, we can find the radius (r) by taking the square root of both sides:
r = √(250 / π)
Once we have the radius, we can calculate the volume of the sphere using the formula:
Volume = (4/3)πr³
Substituting the value of the radius, we can calculate the volume to the nearest tenth of a cubic centimeter.
Explanation: