Question

The radius of a cylindrical gift box is ​(3x +4)) inches. The height of the gift box is twice the radius. What is the surface area of the​ cylinder? Write your answer as a polynomial in standard form.

Answer 1

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