Question

a cartographer is painting a spherical globe whose surface is 326.7 sq in. what is the maximum radius of the globe that the cartographer is painting? use 3.14 for π.

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a sphere is $A = 4\pi r^{2}$, where $A$ is the surface area and $r$ is the radius.

Step2: Substitute given values

We are given that $A=326.7$ square inches and $\pi = 3.14$. Substitute these values into the formula: $326.7=4\times3.14\times r^{2}$.

Step3: Simplify the right - hand side

$4\times3.14 = 12.56$, so the equation becomes $326.7 = 12.56r^{2}$.

Step4: Solve for $r^{2}$

Divide both sides of the equation by $12.56$: $r^{2}=\frac{326.7}{12.56}\approx26$.

Step5: Solve for $r$

Take the square root of both sides: $r=\sqrt{26}\approx 5.1$ inches.

Answer:

$5.1$ in