The answer is 54πx² + 144πx + 96π
The surface area of cylinder (SA) is:
SA = 2 π r h + 2 π r²
The height of the gift box is twice the radius: h = 2r
r = 3x + 4
h = 2(3x + 4) = 6x + 8
SA = 2 π r h + 2 π r²
SA = 2π (r * h + r²)
SA = 2π ((3x + 4)(6x + 8) + (3x + 4)²)
SA = 2π(18x² + 24x + 24x + 32 + 9x² + 24x + 16)
SA = 2π(27x² + 72x + 48)
SA = 54πx² + 144πx + 96π
