The area of the cube face has doubled. How many times has its volume increased?
| November 29, 2020 | education
a – side of a smaller cube, b – side of a larger cube A – face area of a smaller cube, B – face area of a larger cube v – volume of a smaller cube, V – volume of a larger cube 2A = B => 2 * a ^ 2 = b ^ 2 = > √ (2) * a = b => (√ (2) * a) ^ 2 = b ^ 3 => 2 * √ (2) * a ^ 3 = b ^ 3 => 2 * √ (2) * v = V
Answer: 2 √2 times
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