Question

The ratio of the volumes of two cubes is 1 : 8. If the surface area of the smaller cube is 96 cm2, find the surface area of the other cube.

Answer 1

Answer:

Just multiply it 8 by the area of small square

Answer 2

The surface are of larger cube is 864 sq cm  .

Step-by-step explanation:

Given as :

The ratio of the volumes of two cubes is 1 : 8

Let The volume of one cube = v = x

Let The volume of other cube = V = 8 x

The surface area of smaller cube = 96 sq cm

Let The surface area of other cube = A sq cm

Let The each side of smaller cube = a cm

Let The each side of other cube = b cm

According to question

∵ Volume of cube = side³

And The surface area of cube = 6 side²

So, For smaller cube

∵ surface area of cube = 6 side²

So, surface area of smaller cube = 6 a²

Or, 6 a²  = 96

Or,  a² = $\dfrac{96}{6}$

i.e   a² = 16

∴    a = √16 = 4 cm

So, each side of smaller cube = a = 6 cm

Now, Volume of smaller cube = v =  a³

i.e  v = 6³

Or,  volume of smaller cube = 216 cubic cm

Again

The ratio of the volumes of two cubes is 1 : 8

i.e  $\dfrac{volume of small cube}{volume of large cube}$  =   $\dfrac{1}{8}$

or,  $\dfrac{v}{V}$  = $\dfrac{1}{8}$

or, V = 8 × 216   cubic cm

So, Volume of larger cube =  8 × 216   cubic cm

Or, each side of other cube = b  = ∛8 × 216

i.e    b = 12 cm

So, The surface are of larger cube = A =  6 b²

i.e   A = 6 × 12²

∴     A = 864

So, The surface are of larger cube = A =  864 sq cm

Hence , The surface are of larger cube is 864 sq cm  . Answer