The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make right circular cylinder of height 8 cm and base radius 3 cm is

To solve this problem, we need to use the concept of volume conservation. The total volume of the coins will be equal to the volume of the cylinder.

Step 1: Calculate the volume of one coin. The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height (or thickness, in the case of a coin).

For the coin, r = 0.75 cm and h = 0.2 cm. So, the volume of one coin is V = π*(0.75 cm)²*(0.2 cm) = 0.3534 cm³ (approximately).

Step 2: Calculate the volume of the cylinder. For the cylinder, r = 3 cm and h = 8 cm. So, the volume of the cylinder is V = π*(3 cm)²*(8 cm) = 226.195 cm³ (approximately).

Step 3: Calculate the number of coins. The number of coins needed is the volume of the cylinder divided by the volume of one coin. So, the number of coins is 226.195 cm³ / 0.3534 cm³ = 640 (approximately).

So, approximately 640 coins are needed to make the cylinder.