Question

Solve the formula for the radius of a sphere, S = 4πr^2. Then, find the radius of a globe with a surface area of 804 square inches.

a) r = √(S/4π)
b) r = 2√(S/π)
c) r = √(S/π)
d) r = S/(4π)

Answer 1

To solve the radius for a sphere given the surface area S, use the formula r = √(S/4π). Applying this to a surface area of 804 square inches, we can determine the radius of the globe by directly substituting the value into the formula.

Step-by-step explanation:

The student's question is about solving for the radius r of a sphere given the surface area S, using the formula S = 4πr^2. To find the radius from the surface area, we need to isolate r in the equation. The correct transformation would be to divide S by 4π and then take the square root of the result. Therefore, the formula to solve for the radius is:

r = √(S/4π)

Using this formula, for a globe with a surface area of 804 square inches, the radius can be calculated as follows:

r = √(804/4π)

After computing the above expression, we get the radius of the globe. Hence, the correct answer to solve for the radius in terms of the surface area from the given choices would be:

a) r = √(S/4π)