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 = 4(pi)r2 for the surface area of a sphere.
To find the total surface area of the sphere, we can substitute 3x+2 for r in the formula S = 4(pi)r^2:
S = 4(pi)(3x+2)^2
S = 4(pi)(9x^2 + 12x + 4)
S = 36(pi)x^2 + 48(pi)x + 16(pi)
Therefore, the polynomial in standard form that best describes the total surface area of the sphere is:
36(pi)x^2 + 48(pi)x + 16(pi)