Question

$\huge\boxed{\fcolorbox{cyan}{Yellow}{QUESTION:}}$

How many silver coins, 1.75 in a diameter and thickness 2mm, must be melted to form a cuboid of dimensions 55cm x 10cm x 35cm??

$<b><big>NO SPAM$​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• First volume of coin

$\boxed{\sf{Volume\:of\: coin=\pi r{}^{2}h}}$

$\sf\underline{\blue{\:\:\:Given:-\:\:\:\:}}$

$\sf \bullet Radius=\cancel{\dfrac{1.75}{2}}=0.875cm\\ \\ \sf \bullet height=2mm\:\:or\:0.2cm$

Now the volume of coin

$\sf\implies Volume=\pi r{}^{2}h\\ \\ \sf\implies Volume=\dfrac{22}{7}\times 0.875\times 0.875\times 0.2\\ \\ \sf\implies Volume=\dfrac{22\times 0</p><p>875\times 0.875\times 0</p><p>2}{2}\\ \\ \sf\implies Volume=\cancel{\dfrac{3.36875}{2}}=0.</p><p>48125\\ \\ \sf\implies Volume\:of\: coin=0.48125cm{}^{3}$

Now the volume of box

$\boxed{\sf{Volume\:of\: cuboid=l\times b\times h}}$

$\sf\underline{\purple{\:\:\:Given:-\:\:\:\:}}$

●Length=55cm

●Breadth=10cm

●height=35cm

Now the volume

$\sf\implies Volume=l\times b\times h\\ \\ \sf\implies volume=55\times 10\times 35\\ \\ \sf\implies Volume=550\times 35\\ \\ \sf\implies Volume=19250$

Now the number of coins that melts to form box

$\boxed{\sf{No.\:of\: coins=\dfrac{Volume\:of\: box}{Volume\:of\:coin}}}$

$\sf\implies No.\:of\: coins=\dfrac{19250}{0.48125}\\ \\ \sf\implies No.\:of\:coins=40,000$

$\boxed{\sf{\purple{coins\:needed=40000}}}$

Answer 2

Answer:

${\boxed{\bf\red{Coins\:needed=40,000}}}$

Step-by-step explanation:

Given:-

• Diameter of coin = 1.75 cm
• Thickness = 2 mm
• Dimensions of cuboid =55 cm × 10 cm × 35 cm
• Coins needed to be melted= ?

We know that,

${\boxed{\bold\green{Volume\:of\:coin = \pi{r}^{2}h }}}$

${\boxed{\bold\green{Volume\:of\:cuboid=l \times b \times h }}}$

$\rule{300}{2}$

$\sf At\:first, Volume\:of\:cuboid=l \times b \times h$

↓ $\sf Volume\:of\:cuboid = (55\times 10 \times 35)\:{cm}^{3}$

→ ${\boxed{\sf {Volume\:of\:cuboid=19,250\:{cm}^{2} }}}$

$\rule{200}{1}$

$\sf Now, Volume\:of\:coin = \pi{r}^{2}h$

→ $\sf Volume = \dfrac{22}{7} \times {(\dfrac{1.75}{2}) }^{2} \times \dfrac{2}{10}$

→ $\sf Volume = \dfrac{22}{7} \times {0.875}^{2} \times 0.2$

→ $\sf Volume = \dfrac{22}{7} \times 0.765625 \times 0.2$

→ ${\boxed{\sf{Volume\:of\:coin = 0.48125\:{cm}^{3} }}}$

$\rule{200}{1}$

${\boxed{\bold{Coins\:needed=\dfrac{Volume\:of\:cuboid}{Volume\:of\:coin} }}}$

→ $\sf Coins\:needed =\dfrac{19250}{0.48125}$

→ ${\boxed{\sf{Coins\:needed=40,000}}}$