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)
The surface area of the cylinder is given by the formula A = 2πr^2 + 2πrh, where r is the radius and h is the height.
In this case, the radius is 3x – 2 cm and the height is x + 3 cm.
Substituting these values into the formula, we have:
A = 2π(3x – 2)^2 + 2π(3x – 2)(x + 3)
Expanding and simplifying:
A = 2π(9x^2 – 12x + 4) + 2π(3x^2 + 7x – 6)
A = 18πx^2 – 24πx + 8π + 6πx^2 + 14πx – 12π
Combining like terms:
A = (18πx^2 + 6πx^2) + (- 24πx + 14πx) + (8π – 12π)
A = 24πx^2 – 10πx – 4π
The surface area of the cylinder is 24πx^2 – 10πx – 4π.