The radius of a cylinder is 3x - 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A=2 π r^2 + 2 π rh.

a) 2π (3x^2 + 10x - 8)
b) 2π (12x^2 + 7x - 2)
c) 2π (12x^2 - 2x +13)
d) 2π (12x^2 - 5x - 2)

B is the correct option.

Step-by-step explanation:

Given the formula A=2 π r^2 + 2 π rh.

Where radius is 3x - 2 cm and height is

x + 3 cm

Find r^2= (3x -2) (3x -2) = 9x^2 + 4

rh = (3x -2) (x + 3)= 3x^2 + 7x - 6

Slot the values into the formula

A = 2 π (9x^2 + 4) + 2 π (3x^2 + 7x - 6)

Combine the values by adding like terms.

A = 2 π ( 9x^2 + 3x^2 + 7x + 4 - 6)

A = 2 π ( 12x ^2 + 7x - 2), i hope this helps, please mark as brainliest answer.

option D is correct

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

From the information given,

radius = 3x - 2 cm

Height = x + 3 cm

Therefore,

Total surface area =

2 × π × (3x - 2)² + 2 × π × (3x - 2)(x + 3)

= 2π(3x - 2)(3x - 2) + 2π(3x - 2)(x + 3)

= 2π(9x² - 6x - 6x + 4) + 2π(3x² + 9x - 2x - 6)

= 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

= 2π(9x² + 3x² - 12x + 7x + 4 - 6)

= 2π(12x² - 5x - 2)