Calculating the number of coins

To find the number of coins that can be made from a given cylindrical piece of metal, we need to consider the dimensions of the coins and the metal piece.

Dimensions of the coins:
- Diameter of each coin: 1.4 cm
- Thickness of each coin: 0.3 cm

Dimensions of the metal piece:
- Length of the metal piece: 30 cm
- Radius of the metal piece: 14 cm

Calculating the volume of the cylindrical metal piece:
The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.

Given that the radius of the metal piece is 14 cm and the length is 30 cm, we can calculate the volume using the formula as follows:
V_metal = π * (14 cm)^2 * 30 cm
V_metal = π * 196 cm^2 * 30 cm
V_metal = 17640π cm^3

Calculating the volume of each coin:
The volume of a coin can be calculated using the same formula: V = π * r^2 * h. However, in this case, the radius and height will be different as the dimensions of the coin are given.

Given that the diameter of the coin is 1.4 cm and the thickness is 0.3 cm, we can calculate the radius and height as follows:
Radius of the coin = diameter / 2 = 1.4 cm / 2 = 0.7 cm
Height of the coin = thickness = 0.3 cm

Using these values, we can calculate the volume of each coin as follows:
V_coin = π * (0.7 cm)^2 * 0.3 cm
V_coin = π * 0.49 cm^2 * 0.3 cm
V_coin = 0.147π cm^3

Calculating the number of coins:
To find the number of coins that can be made, we need to divide the volume of the metal piece by the volume of each coin.

Number of coins = V_metal / V_coin
Number of coins = (17640π cm^3) / (0.147π cm^3)
Number of coins = 120000

Therefore, 120,000 coins of diameter 1.4 cm and thickness 0.3 cm can be made from a cylindrical piece of metal of length 30 cm and radius 14 cm.

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