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?