Question

two cubes have their volume in the ratio 1:27. The ratio of their surface area is .

Answer 1

Here is your answer:

We know that,

Volume of cube = (side)³

Then ,  

Volume\ of\ Cube_1 = (s_1)^{3}Volume of Cube1​=(s1​)3 

Volume\ of\ cube_2=(s_2)^{3}Volume of cube2​=(s2​)3 


Here s₁ & s₂ are the sides of the Cubes .

Ratio of the volume :

\frac{(s_1)^{3}}{(s_2)^{3}}= \frac{1}{27}(s2​)3(s1​)3​=271​ 

Now take cube root on Both sides.

\frac{S_1}{S_2}= \sqrt[3]{ \frac{1}{27} } = \frac{1}{3}S2​S1​​=3271​​=31​ 

We know that ,

Surface area = 6s².

Then ratio of surface areas :

\frac{6s_1^{2}}{6s_2^{2}} = (\frac{1}{3} )^{2} = \frac{1}{9}6s22​6s12​​=(31​)2=91​ 

Therefore ratio of surface area is 1:9.
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Hope my answer is helpful to you.