Question

A piece of copper is cubical with edge 14 cm. A cylindrical bar of diameter 7 cm is made by melting this piece. What will be the length of this bar ?

Answer 1

Hi there dear user :)

⬇SOLUTION⬇
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We have, edge of the cube = 14 cm = a

Therefore, volume of the cubical piece = a^3 = (14)^3 cm^3 = 14 × 14 × 14 cm^3

Let x cm be the length of the bar in cylindrical shape obtained on melting the cubical piece of copper.

Now, radius of the bar = 7/2 cm (given)

Therefore, volume of the cylindrical bar = pi × r^2 × h = 22/7 × (7/2)^2 × x cm^3

= 22/7 × 7/2 × 7/2 × x cm^3 = 11×7×x/2 cm^3

Since cylindrical bar of x cm length is made by melting the cubical piece of copper, so their volumes must be equal.

Therefore, 11×7×x/2 = 14 × 14 × 14

Therefore, x = 14×14×14×2/11×7 cm = 784/11 cm = 71 3/11 cm

Hence, length of the bar = 71 3/11 cm

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Hope it helps you out ^_^