Question

A cube has a volume of 8 cubic meters. If
each side is doubled in length what will its
new volume be in cubic meters?​

Answer 1

Answer:

64 m³

Step-by-step explanation:

Let each side of cube be a.

Here,

Volume = 8 m³

= > a * a * a = 8 m³

= > a³ = 8 m³

If each side is doubled, new sides are of length 2a.

= > volume = 2a * 2a * 2a

= > volume = 8a³

= > volume = 8(8 m³) = 64 m³

Answer 2

Answer:-

The volume V of a cube is given by the formula:

V = b³

where b is the length of any edge or side of the cube.

• (Remember: All edges or sides of a cube have the same length)

Since it's given that the volume V of a cube of edge or side length b is 8, then, substituting into the above formula, we have:

8 = b³

Now, taking the cube root of both sides we have:

³√8 = ³√b³

2 = b

Now, if we double the length of every side or edge of the cube from b = 2 to b = 4, then volume V becomes:

V = b³

V = 4³

V = (4)(4)(4)

V = (16)(4)

V = 64 cubic units is the volume of a cube if its edges or sides are doubled in length.

So, we see that if the length of the edges or the sides of a cube is doubled, i.e., from b to 2b, then volume V of the cube becomes 8 times as great as before:

64 = 8(8)