4 of 54 of 5 Items Question 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 = 2r2 + 2rh. (1 point) Responses 2(3x2 + 10x – 8) 2 Image with alt text: symbol pi (3 x 2 + 10 x – 8) Image with alt text: 2 pi left-parenthesis 12 x squared plus 7x minus 2 right-parenthesis Image with alt text: 2 pi left-parenthesis 12 x squared minus 2x plus 13 right-parenthesis Image with alt text: 2 pi left-parenthesis 12 x squared minus 5x minus 2 right-parenthesis Skip to navigation
To find the surface area of the cylinder, we need to substitute the given values into the formula A = 2r^2 + 2rh.
The radius of the cylinder is 3x - 2 cm.
The height of the cylinder is x + 3 cm.
Substituting these values into the formula, we get:
A = 2(3x - 2)^2 + 2(3x - 2)(x + 3)
Simplifying this expression gives us:
A = 2(9x^2 - 12x + 4) + 2(3x^2 + 7x - 6)
A = 18x^2 - 24x + 8 + 6x^2 + 14x - 12
A = 24x^2 - 10x - 4
Therefore, the surface area of the cylinder is 24x^2 - 10x - 4.