# Surface Area & Volume Relationships

- Author:
- Aaron Warner, Ryan Poling

## Minimize the Surface Area of the Prism

The square-based prism below has a fixed volume of 36 cm

^{3}. Slide the slider to how the dimensions can change while maintaining the volume. What are the dimensions of the prism with the smallest possible surface area?## Maximize the Volume of the Prism

The square-based prism below has a fixed surface area of 66 cm

^{2}. Slide the slider to how the dimensions can change while maintaining the surface area. What are the dimensions of the cylinder with the largest possible volume?## Minimize the Surface Area of the Cylinder

The cylinder below has a fixed volume of 62.83 cm

^{3}. Slide the slider to how the dimensions can change while maintaining the volume. What are the dimensions of the cylinder with the smallest possible surface area?## Maximize the Volume of the Cylinder

The cylinder below has a fixed surface area of 87.97 cm

^{2}. Slide the slider to how the dimensions can change while maintaining the surface area. What are the dimensions of the cylinder with the largest possible volume?