Question

The volume of a cube in ^3 is equal to twice the surface area of the cube in ^2.
The volume of the cube is ____m^3.
(A) 1336 (B) 1296 (C) 1728 (D) 196

Answer 1

Answer:

Let the side length of the cube be l.

Volume of the cube V=l

3

Surface area of the cube S=6l

2

But, V=S (Given)

Or l

3

=6l

2

⟹ l=6 m

Thus, volume of the cube V=l

3

=6

3

m

3

=216 m

3

Answer 2

Answer:

c.) 1728 m³

Step-by-step explanation:

Given:

• The volume of a cube in m³ is equal to twice the surface area of the cube in m².

To find:

• The volume of cube.

Solution:

To find the volume of cube first we need to find the length of one side of a cube. Sfter substituting the value of length one side of a cube in a volume of cube, we can easily find out the required volume.

Steps...

Let 'a' be the Length of one side of a cube.

Formulae:

♦ Volume of a cube = a³

♦ Surface area of a cube = 6a²

According to the problem,

• a³ = 2 × 6a² ( Twice the surface area means 2 will be multiplied by the surface area )
• a³ = 12a²
• a = 12 m

∴ The Length of one side of a cube = 12 m

Now, find out the volume of cube.

• Volume of a cube = 12³
• Volume of a cube = 12 × 12 × 12
• Volume of a cube = 144 × 12
• Volume of a cube = 1728 m³

∴ The volume of a cube = 1728 m³

____________________________