Question

A sphere has a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for surface area of a sphere.

Answer 1

Start with the given formula for the surface area of a sphere.

$S = 4 \pi r^2$

Now substitute 2x + 5 in for r, the radius.
Then simplify the expression and write it in standard form.

$S = 4 \pi (2x + 5)^2$

$S = 4 \pi (4x^2 + 20x + 25)$

$S = 16 \pi x^2 + 80 \pi x + 100 \pi$