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Three metal cubes of sides 6 cm, 8 cm and 10 cm are melted and recast into a big cube. Find its total surface area.. |
Answer»
According to the question, Three cubes of metal whose edges are 5 cm, 8 cm and 10cm are melted to form a single cube. First cube of edge = 6 cm The volume of the cube = a³ ➝ a × a × a ➝ 6 × 6 × 6 ➝ 36 × 6 ➝ 216 cm³ Second cube of edge = 8 cm The volume of the cube = a³ ➝ a × a × a ➝ 8 × 8 × 8 ➝ 64 × 8 ➝ 512 cm³ Third cube of edge = 10 cm The volume of the cube = a³ ➝ a × a × a ➝ 10 × 10 × 10 ➝ 100 × 10 ➝ 1000 cm³ The volume of the Big cube form by combining the three cubes = Vol of cube 1 + Vol of cube 2 + Vol of cube 3 ➝ 216 + 512 + 1000 ➝ 728 + 1000 ➝ 1728 cm³ The volume of the new cube is 1728 . We know that, The volume of the cube is a³. ➝ a³ = 1728 ➝ a = ➝ a = 12 cm The edge of the new cube is 12 cm . TSA of cube = 6a² ➝ 6 × 12 × 12 ➝ 6 × 144 ➝ 864 cm² ______________________________________ |
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