The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
The diameter of the gold coins is 4 cm, so the radius is half of that, or 2 cm. The height is given as 1 cm.
The volume of one coin can be calculated as follows:
V = πr^2h = π(2 cm)^2(1 cm) = 4π cm^3
Therefore, the volume of one coin is 4π cubic centimeters.
If each of the six kids takes seven coins, then the total number of coins taken is 6 × 7 = 42 coins.
The total volume of all the coins they take back can be calculated as follows:
Total volume = volume of one coin × number of coins
Total volume = 4π cm^3 × 42
Total volume = 168π cubic centimeters
Therefore, the total volume of all the gold coins they take back is 168π cubic centimeters.