Math Snap

STEP 1

1. The mean length of six rods is $44.2 \, \text{cm}$.
2. The mean length of five of these rods is $46 \, \text{cm}$.
3. We need to find the length of the sixth rod.

STEP 2

1. Calculate the total length of all six rods.
2. Calculate the total length of the five rods.
3. Determine the length of the sixth rod.

STEP 3

Calculate the total length of all six rods using the mean:
$$\text{Total length of six rods} = 44.2 \times 6$$ $$= 265.2 \, \text{cm}$$

STEP 4

Calculate the total length of the five rods using their mean:
$$\text{Total length of five rods} = 46 \times 5$$ $$= 230 \, \text{cm}$$

Determine the length of the sixth rod by subtracting the total length of the five rods from the total length of all six rods:
$$\text{Length of sixth rod} = 265.2 - 230$$ $$= 35.2 \, \text{cm}$$ The length of the sixth rod is:
$$\boxed{35.2 \, \text{cm}}$$