A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

1 : 6

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1 : 5

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1 : 25

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1 : 125

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Solution

The correct option is B $1 : 5$
Number smaller cubes $= \frac{{(5)}^{3}}{{(1)}^{3}} = 125$
Now, $\frac{S_{1}}{S_{2}} = \frac{6 \times 5^{2}}{6 \times {(1)}^{2} \times 125} = \frac{25}{125} = \frac{1}{5} = 1 : 5$

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A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

The correct option is B 1:5Number smaller cubes =(5)3(1)3=125Now, S1S2=6×526×(1)2×125=25125=15=1:5

The correct option is B $1 : 5$
Number smaller cubes $= \frac{{(5)}^{3}}{{(1)}^{3}} = 125$
Now, $\frac{S_{1}}{S_{2}} = \frac{6 \times 5^{2}}{6 \times {(1)}^{2} \times 125} = \frac{25}{125} = \frac{1}{5} = 1 : 5$