Question

Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is
(b) 1:8
(c) 1:9
(d) 1:18
(a) 1:13

Answer 1

Answer:

Option c 1:9 is your answer

Answer 2

Answer:

If two cubes have their volumes in the ratio 1:27, then the ratio of their surface areas is 1: 9.

Step-by-step explanation:

If the side of the first cube is $a_1$.

and the side of the second cube is $a_2$.

And the volume of the first cube = $v_1$

and the volume of the second cube = $v_2$

As per the given condition

$\frac{v_1}{v_2} = \frac{a_1^3}{a_2^3} \\\frac{1}{27} =\frac{a_1^3}{a_2^3} \\\frac{a_1}{a_2} =\frac{1}{3}$

Now the ratio of surface areas

$\frac{S_1}{S_2} = \frac{6a_1^2}{6a_2^2} \\\frac{S_1}{S_2} = \frac{ a_1^2}{ a_2^2} \\\frac{S_1}{S_2} = \frac{ 1^2}{ 3^2} \\\frac{S_1}{S_2} = \frac{ 1}{ 9}$

So, the ratio of their surface areas is is 1: 9.