14. A Cylindrical can has a height of 12 cm and a diameter of 6 cm . a) Calculate the volume. (show your formula) b) Calculate the surface area. Draw a sketch of the can. (show your formula)

To calculate the volume and surface area of the cylindrical can, we can use the following formulas: a) Volume of a cylinder: \[ V = \pi r^2 h \] b) Surface area of a cylinder: \[ A = 2\pi r^2 + 2\pi rh \] Given: - Height of the cylinder (\( h \)) = 12 cm - Diameter of the cylinder (\( d \)) = 6 cm - Radius of the cylinder (\( r \)) = \( \frac{d}{2} \) = 3 cm a) Calculate the volume: \[ V = \pi \times 3^2 \times 12 \] b) Calculate the surface area: \[ A = 2\pi \times 3^2 + 2\pi \times 3 \times 12 \] Let's calculate the volume and surface area using the given formulas. Calculate the value by following steps: - step0: Calculate: \(\pi \times 3^{2}\times 12\) - step1: Multiply the terms: \(9\pi \times 12\) - step2: Multiply the terms: \(108\pi \) a) The volume of the cylindrical can is approximately 339.29 cm³. b) Calculate the surface area: \[ A = 2\pi \times 3^2 + 2\pi \times 3 \times 12 \] Let's calculate the surface area. Calculate the value by following steps: - step0: Calculate: \(2\pi \times 3^{2}+2\pi \times 3\times 12\) - step1: Multiply the terms: \(18\pi +2\pi \times 3\times 12\) - step2: Multiply the terms: \(18\pi +72\pi \) - step3: Collect like terms: \(\left(18+72\right)\pi \) - step4: Add the numbers: \(90\pi \) b) The surface area of the cylindrical can is approximately 282.74 cm². The volume of the cylindrical can is approximately 339.29 cm³, and the surface area is approximately 282.74 cm².