What is the surface area of a cylindrical can with a radius of 3 centimeters and a height of 11 centimeters?

To find the surface area of a cylindrical can, we need to calculate 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: \[ \text{Surface Area} = 2 \pi r^2 + 2 \pi r h \] Where: - \( r \) is the radius of the cylinder - \( h \) is the height of the cylinder Given: - Radius (\( r \)) = 3 centimeters - Height (\( h \)) = 11 centimeters Substitute the values into the formula: \[ \text{Surface Area} = 2 \pi (3)^2 + 2 \pi (3) (11) \] Now, we can calculate the surface area. Calculate the value by following steps: - step0: Calculate: \(2\pi \times 3^{2}+2\pi \times 3\times 11\) - step1: Multiply the terms: \(18\pi +2\pi \times 3\times 11\) - step2: Multiply the terms: \(18\pi +66\pi \) - step3: Collect like terms: \(\left(18+66\right)\pi \) - step4: Add the numbers: \(84\pi \) The surface area of the cylindrical can with a radius of 3 centimeters and a height of 11 centimeters is approximately 263.893783 square centimeters.