Question

The volume of two cubes are in the ratio 8:64, the ratio of their surface areas is
(a) 1:4
(6) 4:1
(c) 1:1
(d) 4:3
answer fast ​

Answer 1

The correct option is option (a)

Therefore the ratio of their surface area is 1:4

Step-by-step explanation:

Given that the volume of two cubes are in the ratio 8:64.

Let the length of side of 1st cube be x unit and second cube be y unit.

Then ,

The volume of first cube is = x³ cube units

and the volume of second cube be =y³cube units

According to the problem,

$\frac{x^3}{y^3} =\frac{8}{64}$

$\Rightarrow \frac{x}{y} =\sqrt[3]{\frac{8}{64} }$

$\Rightarrow \frac{x}{y} =\frac{2}{4}$

⇒x:y= 2:4

Let the length of side of first cube be 2a and

second cube be 4a.

The surface area of a cube = 6×side²

The surface area of the first cube = [6×(2a)²] square units

                                                        =[6×4a²] square units

The surface area of the second cube=[6×(4a)²] square units

                                                             =[6×16a²] square units

Therefore the ratio of their surface area

=[6×4a²]:[6×16a²]

=4:16

=1:4