4. 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?
2spi (3x2 + 10x – 8)
2 pi (12x2 + 7x-2)
2 pi (12x2 -2x +13)
2 pi (12x2 -5x -2)* my answer??
found the right answer -- the last one.
To find the surface area of a cylinder, we need to find the area of the two circular bases and the area of the curved surface.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values into the formula:
Surface Area = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
Simplifying this expression gives:
Surface Area = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
Next, we can distribute the 2π to both terms inside the parentheses:
Surface Area = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
Combining like terms gives:
Surface Area = (18πx² + 6πx²) + (-24πx + 14πx) + (8π - 12π)
Simplifying further gives:
Surface Area = 24πx² - 10πx - 4π
So, none of the provided options is the correct answer. The correct answer would be 24πx² - 10πx - 4π.