Question

The surface area S of a sphere with radius r is give by the formula S = 4(3.14)r². Solve the formula for r. Then find the radius of a globe with a surface area of 804 square inches.

Answer 1

The formula for the surface area of a sphere is rearranged to solve for radius 'r', and then applied to find the radius of a globe with a given surface area. For a globe with a surface area of 804 square inches, the radius is approximately 8.99 inches.

Step-by-step explanation:

Solving the Formula for Radius

To find the radius r from the surface area formula S = 4(3.14)r², you can use the following steps:

1. First, divide both sides of the formula by 4(3.14) to get r² = S / (4 * 3.14).
2. Next, take the square root of both sides to solve for r. This gives you r = √(S / (4 * 3.14)).

Applying this to a globe with a surface area of 804 square inches, you:

1. Insert the value of S into the formula, obtaining r as r = √(804 / (4 * 3.14)).
2. Calculate the numerical answer to find r, which in this case is approximately 8.99 inches.

Understanding Geometric Formulae

Remember, the formulae for a sphere for volume is 4/3 (pi) (r)³ and for surface area is 4 (pi) (r)². The student's question refers to the surface area formula, which is used to solve for the radius given the surface area.