Question

Find the least number of coins of diameter 2.5 cm and height 3 mm which are to be
melted to form a solid cylinder of radius 3 cm and height 5 cm.​

Answer 1

Given:

✰ Diameter of each coin = 2.5 cm

✰ Height of each coin = 3 mm = 0.3 cm

✰ Radius of solid cylinder = 3 cm

✰ Height of solid cylinder = 5 cm

To find:

✠ The least number of coins which are to be melted to form a solid cylinder.

Solution:

Let's understand the concept first!

• First we will find the volume of each coin as we are provided with a diameter, we will find out the radius of a coin and we already have the height. By using the formula of volume, we will find its volume.
• Then we will find the volume of a cylinder by using formula. Putting the values in the formula and then doing the required calculations.
• After that we will divide the volume of a cylinder by the volume of each coin to find out the number of least number of coins which are to be melted to form a solid cylinder.

Let's find out...✧

⇾ Radius of each coin = Diameter/2

⇾ Radius of each coin = 2.5/2

⇾ Radius of each coin = 5/4 cm

✭ Volume of each coin = πr²h ✭

Putting the values in the formula, we have:

➛ Volume of each coin = 22/7 × (5/4)² × 0.3

➛ Volume of each coin = ( 22/7 × 25/16 × 0.3 ) cm³

✭ Volume of cylinder = πR²h ✭

Putting the values in the formula, we have:

➛ Volume of solid cylinder = 22/7 × 3² × 5

➛ Volume of solid cylinder = 22/7 × 9 × 5

➛ Volume of solid cylinder = ( 22/7 × 45 ) cm³

Now,

➤ The least number of coins to be needed = Volume of solid cylinder/Volume of each coin

➤ The least number of coins to be needed = (22/7 × 45)/(22/7 × 25/16 × 0.3)

➤ The least number of coins to be needed = 45/(25/16 × 0.3)

➤ The least number of coins to be needed = 450/(25/16 × 3)

➤ The least number of coins to be needed = 96

∴ 96 coins which are to be melted to form a solid cylinder.

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Answer 2

Given:

✰ Diameter of each coin = 2.5 cm

✰ Height of each coin = 3 mm = 0.3 cm

✰ Radius of solid cylinder = 3 cm

✰ Height of solid cylinder = 5 cm

To find:

✠ The least number of coins which are to be melted to form a solid cylinder.

Solution:

Let's understand the concept first!

First we will find the volume of each coin as we are provided with a diameter, we will find out the radius of a coin and we already have the height. By using the formula of volume, we will find its volume.

Then we will find the volume of a cylinder by using formula. Putting the values in the formula and then doing the required calculations.

After that we will divide the volume of a cylinder by the volume of each coin to find out the number of least number of coins which are to be melted to form a solid cylinder.

Let's find out...✧

⇾ Radius of each coin = Diameter/2

⇾ Radius of each coin = 2.5/2

⇾ Radius of each coin = 5/4 cm

✭ Volume of each coin = πr²h ✭

Putting the values in the formula, we have:

➛ Volume of each coin = 22/7 × (5/4)² × 0.3

➛ Volume of each coin = ( 22/7 × 25/16 × 0.3 ) cm³

✭ Volume of cylinder = πR²h ✭

Putting the values in the formula, we have:

➛ Volume of solid cylinder = 22/7 × 3² × 5

➛ Volume of solid cylinder = 22/7 × 9 × 5

➛ Volume of solid cylinder = ( 22/7 × 45 ) cm³

Now,

➤ The least number of coins to be needed = Volume of solid cylinder/Volume of each coin

➤ The least number of coins to be needed = (22/7 × 45)/(22/7 × 25/16 × 0.3)

➤ The least number of coins to be needed = 45/(25/16 × 0.3)

➤ The least number of coins to be needed = 450/(25/16 × 3)

➤ The least number of coins to be needed = 96

∴ 96 coins which are to be melted to form a solid cylinder.

_______________________________

Step-by-step explanation:

Hope this answer will help you.✌️