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Two cubes have their volumes in the ratio 1 : 125. Find the ratio of their surface areas.
Question

Two cubes have their volumes in the ratio 1 : 125. Find the ratio of their surface areas.

A.

1 : 125

B.

1 : 25

C.

25 : 1

D.

1 : 5

Correct option is B

Given:
Ratio of volume of two cubes = 1:125
Formula Used:
Volume of cube = a3a^3​​
Total surface area of cube =  6a26a^2​​
where a is side of cube
Solution:
Ratio = ((Volume of one cube)/(Volume of second cube)) = (a13)(a23)=1125\frac{(a_1^3)}{(a_2^3 )} = \frac{1}{125}​​
Taking cube root both sides
(a13)(a23)=1125)  a1a2=15\sqrt{\frac{ (a_1^3)}{(a_2^3 )}}=\sqrt\frac{1}{125}) \\\ \\\ \frac{a_1}{a_2} =\frac{1}{5}​​
Ratio of their surface areas =  (a12)(a22)=(15)2=125\frac{(a_1^2)}{(a_2^2 )} = (\frac{1}{5})^2 = \frac{1}{25}​​

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