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प्रश्न
Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is ______.
विकल्प
12 cm
24 cm
18 cm
20 cm
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उत्तर
Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is 12 cm.
Explanation:
The edges of three cubes are 6 cm, 8 cm and 10 cm, respectively.
∴ Sum of volumes of the three metal cubes
= 63 + 83 + 103 ...[∵ Volume of cube = (edge)3]
= 216 + 512 + 1000
= 1728 cm3
Since, a new cube is formed by melting these three cubes.
Let a be the side of new cube. Then,
Volume of the new cube = Sum of volumes of three metal cubes
⇒ a3 = 1728
∴ a = 12 cm
Hence, the edge of the new cube is 12 cm.
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