(c) the cylinder is open on top and the dimensions are radius \( =3 \mathrm{~cm} \) and height \( =5 \mathrm{~cm} \)

To find the surface area and volume of an open-top cylinder with a radius of \(3 \, \text{cm}\) and a height of \(5 \, \text{cm}\), we can use the following formulas: ### Volume of the Cylinder The volume \( V \) of a cylinder is given by the formula: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. Substituting the given values: \[ V = \pi (3 \, \text{cm})^2 (5 \, \text{cm}) = \pi (9 \, \text{cm}^2)(5 \, \text{cm}) = 45\pi \, \text{cm}^3 \] ### Surface Area of the Open-Top Cylinder The surface area \( A \) of an open-top cylinder consists of the area of the base and the lateral surface area. The formula is: \[ A = \text{Base Area} + \text{Lateral Surface Area} \] 1. **Base Area**: The area of the base is given by: \[ \text{Base Area} = \pi r^2 = \pi (3 \, \text{cm})^2 = 9\pi \, \text{cm}^2 \] 2. **Lateral Surface Area**: The lateral surface area is given by: \[ \text{Lateral Surface Area} = 2\pi rh = 2\pi (3 \, \text{cm})(5 \, \text{cm}) = 30\pi \, \text{cm}^2 \] Now, adding these two areas together: \[ A = 9\pi \, \text{cm}^2 + 30\pi \, \text{cm}^2 = 39\pi \, \text{cm}^2 \] ### Summary - **Volume**: \( 45\pi \, \text{cm}^3 \) (approximately \( 141.37 \, \text{cm}^3 \)) - **Surface Area**: \( 39\pi \, \text{cm}^2 \) (approximately \( 122.52 \, \text{cm}^2 \))