Question

A cube has numerically equal volume and surface area. The volume of such cube is
(a)216 units
(b) 1000 units
(c) 2000 units
(d) 3000 unts

Answer 1

Given volume of cube = surface area of cube

a3 = 6a2

⇒ a = 6

Hence volume of cube = 63

= 216 cubic units

Answer 2

The volume of the cube is 216 units. (Option a)

Given,

A cube has equal surface area and volume

To Find,

The volume of the cube

Solution,

Let the side of the cube be 'a'

Then, its volume will be a³

A cube has 6 surfaces, therefore its surface area is 6a²

According to the question,

a³ = 6a²

$\frac{a^3}{a^2}$ = 6

a = 6

So, we get the side of the cube as 6 units

Now, the volume of the cube will be -

Volume = a³

Volume = 6 x 6 x 6

Volume = 216 units

Thus, the volume of the cube is 216 units.

#SPJ3