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1). 484 cm32). 625 cm33). 729 cm34). Cannot be determined |
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Answer» Let the side of the ORIGINAL cube = ‘X’ cm Side of the new cube = (x - 4) cm Difference between the original and new volume = 604 x3 - (x - 4)3 = 604 ⇒ x3 - (x3 + 48X - 12x2 - 43) = 604 ⇒ x3 - (x3 + 48x - 12x2 - 64) = 604 ⇒ x3 - x3- 48x + 12x2 + 64 = 604 ⇒ 12x2 - 48x + 64 - 604 = 0 ⇒ 12x2 - 48x - 540 = 0 ⇒ x2 - 4x - 45 = 0 ⇒ x2 - 9X + 5x - 45 = 0 ⇒ x(x - 9) + 5(x - 9)= 0 ⇒ (x + 5) (x - 9) = 0 ⇒ (x + 5) = 0 or (x - 9) = 0 ⇒ x = -5 or x = 9 Volume = (Side)3 = (9)3 = 729 cm3 ∴ Volume of the original cube = 729 cm3 |
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