Question

A sphere has a radius of 3x + 2. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4πr^2 for surface area of a sphere.
A. 16πx^2 + 16π
B. 16πx^2 + 48π + 16π
C. 36πx^2 + 48πx + 16π
D. 36πx^2 + 24πx + 16π

Please include steps, thank you.

Answer 1

To find the total surface area of the sphere, we will substitute the given radius into the formula for surface area:

S = 4π(3x + 2)^2
S = 4π(9x^2 + 12x + 4)
S = 36πx^2 + 48πx + 16π

Therefore, the polynomial in standard form that best describes the total surface area of the sphere is:

C. 36πx^2 + 48πx + 16π.