Question

Ratio of surface areas of two cubes is 1:4. Find the ratio of their volumes.

Answer 1

Question

Ratio of surface areas of two cubes is 1:4. Find the ratio of their volumes.  

Answer

Ratio of the cubes Surface Area - 1:4

Total Surface area of cube 1 → 6a²

Total Surface area of cube 2 → 6x²

Surface area = 1:4, now we equate the formula to the value, to find the value of the sides.

$\implies \mathsf{\frac{6a^{2}}{6x^{2}}}} = \frac{1}{4}$

[6 gets cancelled]

$\implies \mathsf{\frac{a^{2}}{x^{2}}}} = \frac{1}{4}$

$\implies \mathsf{\frac{a}{x}} = \sqrt{{\frac{1}{4}$

$\implies \mathsf{\frac{a}{x}} = \frac{1}{2}$

a : x = 1 : 2

Hence,

a = 1

x = 2

Now, Volumes are ↓

Formula for finding Volume = a³

Vol. Of Cube 1

= a³

= 1³

= 1

Vol. Of Cube 2

= a³

= 2³

= 8

Hence the ratio of their volumes is 1:8.

Answer 2

Answer:

Two cubes =1x/4x

TSA of cube1 =6a2

TSA of cube2 =6x2

so,

=6a2/6x2 = 1/4

(6 is cancelled now)

=a/x = 1/2

=a:x = 1:2

Volume of one cube = a3 = 1^3 = 1

Volume of second cube = a3 = 2^3 = 8

so,

The ratio of their volumes = 1:8