Question

How many coins of diameter 1.75 cm and thickness 2 cm can be made by melting down a cuboid of sides 5.5 cm, 10 cm and 3.5 cm?​

Answer 1

Correction in the Question:

How many coins of diameter 1.75 cm and thickness 2 mm can be made by melting down a cuboid of sides 5.5 cm, 10 cm and 3.5 cm?​

Solution:

Dimensions of the cylindrical coins to be made:

• Diameter (d) = 1.75 cm.
• Radius (r) = (1.75)/2 cm.
• Height (H) = 2 mm → 2/10cm.

Dimensions of the cuboid:

• Assuming the sides are a, b & c;
• a = 5.5 cm.
• b = 10 cm.
• c = 3.5 cm.

Let "n" be the number of coins that have to be made.

Therefore, Volume of one cylindrical coin multiplied by "n" is equal to the volume of the cuboid.

$\longmapsto \sf Volume \ of \ a \ Cylinder = \pi r^2h\\ \\ \\\longmapsto \sf Volume \ of \ a \ Cuboid = l \times b \times h$

Therefore,

$\Longrightarrow \sf l \times b \times h = n \times \pi r^2 H\\ \\ \\\Longrightarrow \sf 5.5 \times 10 \times 3.5 = n \times \dfrac{22}{7} \times \Bigg( \dfrac{1.75}{2} \Bigg)^2 \times \dfrac{2}{10} \\ \\ \\ \\\Longrightarrow \sf 192.5 = n \times \dfrac{22}{7} \times \dfrac{1.75}{2} \times \dfrac{1.75}{2} \times \dfrac{2}{10} \\ \\ \\ \\\Longrightarrow \sf 192.5 = n \times \dfrac{11}{70} \times 1.75 \times 1.75$

$\Longrightarrow \sf \dfrac{192.5 \times 70}{11 \times 1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{17.5 \times 70}{1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{1225}{1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{700}{1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{700}{1.75} \times \dfrac{100}{100} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{70000}{175} = n \\ \\ \\ \\\Longrightarrow \sf n = 400$

Therefore, the number of coins that can be made is 400.

Answer 2

Given:-

• Diameter (d) of cylinderical coin = 1.75cm

∴ Radius (r) = Diameter/2 = 1.75/2

• Thickness (h) of coin = 2 cm

_______________________________

• Length (l) of cubiod = 5.5 cm

• Breadth (b) of cubiod = 10 cm.

• Height (h) of cuboid = 3.5 cm

To Find:-

• No. of coins made by melting of given cuboid.

Solution:-

Firstly ,we have to find the volume of a coin .

So, by applying this formula

☛ Vol. of cylindrical coin = πr²h

putting all the values which is given above

vol. of coin = 22/7 × 1.75/2 × 1.75 × 2

vol. of coin = 4.8125 cm3

And Now, we have also calculate the volume of cuboid .

☛ vol. of cuboid = l × b × h

putting all the values which is given above

vol. of cuboid = 5.5 × 10 × 3.5

vol. of cuboid = 192.5

Now we have to find the no. of coin which is made by melting of cuboid

∴ No. of coin = vol. of cuboid / vol. of coin

No. of coin = 192.5/4.8125

No. of coin = 40

∴ The number of coins which is made by melting of cuboid = 40 coins.