Question

a sphere has a radius of 3x+2. which polynomial in standard form. best describes the total surface area of the sphere

Answer 1

The answer is 36πx² + 48πx + 16π.

The surface area of the sphere with radius r is:
A = 4 π r²

r = 3x+2
A = 4 π (3x+2)²

Since (a+b)² = a² + 2ab + b², then (3x+2)² = (3x)² + 2 * 3x * 2 + 2² = 9x² + 12x + 4

A = 4π*(3x+2)² =
    = 4π*(9x² + 12x + 4) = 
    = 4π*9x² + 4π*12x + 4π*4 = 
    = 36πx² + 48πx + 16π