Question:
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface areas of the original cube to that of the sum
of the surface areas of the smaller cubes?
Solution:
Surface area of a cube = 6 a2, where a is side of a cube.
... Side of cube = 5cm
... Surface area of the cube = 6 x (5)2 = 6 x 25
= 150cm2
Now, surface area of the cube with side 1 cm = 6 x (1)2= 6 cm2
... Surface area of 5 cubes with side 1 cm = 5 x 6 = 30 cm2
Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes
=30/150=3/15=1:5
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