Final answer:
A 17cm pencil can fit inside a cube-shaped box with 10cm sides because the diagonal of the cube is about 17.32cm, which is longer than the pencil.
Step-by-step explanation:
The question asks whether a pencil that is 17cm long will fit inside a cube-shaped box with side lengths of 10cm. To answer this, we must determine the longest line segment (the diagonal) that can fit inside the cube. The formula for the space diagonal of a cube is √3 times the length of one side. In this case:
- The formula is √3 x 10cm, which is approximately 17.32cm.
- So, a pencil that is 17cm long will indeed fit inside the box, as the space diagonal is slightly larger than the pencil's length.
Therefore, based on the calculation of the cube's space diagonal, we can confirm that the pencil can fit diagonally within the cube-shaped box.