Calculate the lateral surface area, total surface area, and volume of a right circular cylinder with radius 4 cm and height 10 cm.

The formula for the lateral surface area of a cylinder is $LSA = 2 \pi r h$.

$$LSA = 2 \pi (4 \text{ cm})(10 \text{ cm})$$ $$LSA = 80 \pi \text{ cm}^2$$

The lateral surface area is $\boxed{80 \pi \text{ cm}^2}$.

The formula for the total surface area of a cylinder is $TSA = 2 \pi r (h + r)$.

$$TSA = 2 \pi (4 \text{ cm})(10 \text{ cm} + 4 \text{ cm})$$ $$TSA = 8 \pi \text{ cm}(14 \text{ cm})$$ $$TSA = 112 \pi \text{ cm}^2$$

The total surface area is $\boxed{112 \pi \text{ cm}^2}$.

The formula for the volume of a cylinder is $V = \pi r^2 h$.

$$V = \pi (4 \text{ cm})^2 (10 \text{ cm})$$ $$V = \pi (16 \text{ cm}^2)(10 \text{ cm})$$ $$V = 160 \pi \text{ cm}^3$$

The volume is $\boxed{160 \pi \text{ cm}^3}$.