Surface Areas & Volumes | Exercise 13.5 | Q8

CBSE Class 9 Maths NCERT Exercise Solutions | Cubes | Volume & Surface Areas

Question 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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Explanatory Answer | Exercise 13.5 Q8

Step 1: Compute the side of the new cube

Side of the larger cube, a = 12 cm
Volume of the larger cube = a3
= 123
= 1728 cm3

Volume of 8 small new cubes = Volume of the large cube
Let s be the side of the small new cubes.
Volume of each small cube = s3
Therefore, 8 × s3 = 1728
Or s3 = \\frac{1728}{8})
s3 = 216
s = 6 cm

Step 2: Compute the surface area of the cubes

Side of each small cube, s = 6 cm; side of large cube = 12 cm.
Surface area of large cube = 6 a2 = 6 × 122
Surface area of small cube = 6 s2 = 6 × 62
Ratio of their surface areas = \\frac{6×122}{6×6^2})
= \\frac{12×12}{6×6})
= \\frac{4}{1})
Ratio of their surface areas = 4 : 1

 


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