The Pythagorean Theorem in Three Dimensions Practice Complete this assessment to review what you've learned. It will not count toward your grade. A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm . What is the longest straw that can fit completely inside the juice can diagonally? Round the answer t the nearest tenth. (1 point)

To find the longest straw that can fit diagonally inside the juice can, we can use the 3D version of the Pythagorean theorem. First, we'll consider the can as a rectangular prism where the diagonal distance (d) can be calculated using the formula: \[ d = \sqrt{h^2 + r^2} \] where h is the height and r is the radius of the can. Substituting the values: Height (h) = 122 mm Diameter = 52 mm, thus Radius (r) = 52/2 = 26 mm. So, we calculate: \[ d = \sqrt{122^2 + 26^2} \] \[ d = \sqrt{14884 + 676} \] \[ d = \sqrt{15560} \] \[ d \approx 124.8 \text{ mm} \] Rounding to the nearest tenth, the longest straw that can fit inside the juice can is approximately **124.8 mm**. For a fun fact, did you know the Pythagorean theorem has been recognized for over 2,500 years and is used not just in math but in fields like architecture and engineering? It's practical for everything from designing buildings to ensuring safety in structures! Moreover, when dealing with dimensions and shapes, it’s important to visualize the scenarios. To avoid mistakes, sketching the can and marking the height and diameter can help in grasping the relationship better, ensuring you remember to use the radius in calculations instead of the diameter directly!