Question

एक घनाभ जिसकी भुजाओं 5.5 सेमी. 10 सेमी. और 3.5 सेमी. हैं, तो पिघलाकर सेमी. व्यास तथा 2 सेमी. मोटाई के कितने सिक्के बनाए जा सकते हैं?​

Answer 1

Given:

एक घनाभ जिसकी भुजाओं 5.5 सेमी. 10 सेमी. और 3.5 सेमी. हैं|

To find:

तो पिघलाकर 1.75 सेमी. व्यास तथा 2 मीमी. मोटाई के कितने सिक्के बनाए जा सकते हैं?​

Solution:

The dimensions of the cuboid:

Length, l = 5.5 cm

Breadth, b = 10 cm

Height, h = 3.5 cm

∴ The volume of the cuboid = l × b × h = 5.5 × 10 × 3.5 = 192.5 cm³

The dimensions of each coin:

Diameter = 1.75 cm

∴ Radius, r = $\frac{1.75 }{2} = 0.875$

Thickness or Height, h = 2 mm = 0.2 cm

∴ The volume of each coin = $\pi r^2 h = \frac{22}{7} \times 0.875^2 \times 0.2 = 0.481 \:cm^3$

Now,

The required no. of coins on melting the cuboid will be,

= $\frac{Volume\:the\:cuboid}{Volume\:of\:each\:coin}$

= $\frac{192.5}{0.481}$

= 400.20

≈ 400

Thus, 400 coins can be made by melting the cuboid.

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