Question

when an iron rod is cut into equal pieces of 30 cm each , a peice of 4 cm is left out . when cut into equal peice of 29 cm each ,a peice of 13 cm is left out. if the cross sectional area of the rod is 1 cm^2 . find the minimum volume of the rod​

Answer 1

Answer:

First we find minimum length of rod

This question is same as smallest positive integer gives remainder of 4 dividing by 30 and 13 dividing by 29 . So

$30m + 4 = 29n + 13 \\Note\: n \geq m\\ 30m = (30 - 1)n + 9 \\ \\30(m - n) = 9 - n \\\\ 30(n - m) = n - 9 \\\\ n = 30k + 9 \: \: ,\: \: k \geqslant 0\\\\ smallest \:\: when \:\:k=0\\</p><p>n = 9$

so length will be 30×9 + 4 = 274

So volume = Al = 1 × 274 = 274 cm3