what is the tricky way for solving the question of class 9th ncert math of Surface areas and Volumes chapter of ncert of exercise 13.5 of math give me the best and simple way for solving this question in easy and simple way of question no 8 A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas
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A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas. Q.8
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Side of a cube = 12cm (Given)
Find the volume of cube:
Volume of cube = (Side)3 = (12)3cm3= 1728cm3
Surface area of a cube with side 12 cm = 6a2 = 6(12) 2 cm2 …(1)
Cube is cut into eight small cubes of equal volume, say side of each cube is p.
Volume of a small cube = p3
Surface area = 6p2 …(2)
Volume of each small cube = (1728/8) cm3 = 216 cm3
Or (p)3 = 216 cm3
Or p = 6 cm
Now, Surface areas of the cubes ratios = (Surface area of bigger cube)/(Surface area of smaller cubes)
From equation (1) and (2), we get
Surface areas of the cubes ratios = (6a2)/(6p2) = a2/p2 = 122/62 = 4
Therefore, the required ratio is 4 : 1.