multiplying binomials

Question

the radius of a cylindrical popcorn tin is (3x+1) in. The height of the tin is three times the radius. What is the surface area of the cylinder? write your answer in symplified form

Answer 1

Surface area is the area of the top and bottom added to

the product of the circumference and height

 

SA = 2(pi)r² + 2(pi)rh

 

r = 3x+1

h = 3(3x+1) = 9x + 3

 

SA = 2(pi)(3x+1)² + 2(pi)(3x+1)(9x+3)

 

= 2(pi)(9x² + 6x + 2) + 2(pi)(27x² + 18x + 3)

 

= 18(pi)x² + 12(pi)x + 4(pi) + 54(pi)x² + 36(pi)x + 6(pi)

 

= 72πx² + 48πx + 10π