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A cubic meter of copper weighing 9000 kg is rolled into a square bar 9 m long. An exact cube is cut off from the bar. How much does it weigh?

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333.3 kg

320.5 kg

349.1 kg

312.9 kg

answer is A.

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Detailed Solution

We assume that a cubic meter of copper weighing 9000 kg is rolled into a square rod of length 9 m.

Let the width (side) of the square bar be ‘a’.
Volume of the copper is one cubic meter,

1 m 3

.
Volume of the square bar is =

9 × a × a = 9 a 2 m 3

The volume of the square bar must be equal to the volume of the copper.

V o l u m e c o p p e r = V o l u m e b a r ​ ⇒ 1 m 3 = 9 a 2 m 3 ​ ⇒ 1 = 9 a 2 ​ ⇒ a 2 = 19 ​ ∴ a = 13 m ​

The side of the square bar is

13 m

.
Therefore, the edge of the cut-off cube from the square bar will also be

13 m

.
Volume of the cube is

13 × 13 × 13 = 127 m 3

1 m 3

weighs 9000 kg, then

127 m 3

weighs

127 × 9000 = 333.3 k g

The weight of the cube is 333.3 kg.
So, the correct answer is Option 1.

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