Question

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

Answer 1

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.

$\begin{gathered}\longmapsto \sf Volume \ of \ a \ Cylinder = \pi r^2h\\ \\ \\\longmapsto \sf Volume \ of \ a \ Cuboid = l \times b \times h\\\end{gathered}$

Therefore,

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

$\begin{gathered}\Longrightarrow \sf \dfrac{192.5 \times 70}{11 \times 1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{17.5 \times 70}{1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{1225}{1.75 \times 1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{700}{1.75} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{700}{1.75} \times \dfrac{100}{100} = n \\ \\ \\ \\\Longrightarrow \sf \dfrac{70000}{175} = n \\ \\ \\ \\\Longrightarrow \sf n = 400 \\ \\ \\\end{gathered} </p><p>$

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

Answer 2

Step-by-step explanation:

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

So, by applying this formula

Vol. of cylindrical coin = r²h

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 = 1 × b xh

Vol 82

putting all the values which is given above

vol. of cuboid = 5.5 × 10 × 3.5 X

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.