如果立方体的长度增加一倍，它的体积会发生什么变化？

立方体是与一定体积相关联的三维形状。它有六个方形面，每个面对应一个相等的长度。它可以被认为是堆叠在一起的正方形片材。也称为正六面体，是五种柏拉图立体形状之一。

立方体的体积

立方体的体积是占据一定质量或空间体积的三维形状。立方体的体积单位为（单位） ³或立方单位。 SI 的体积单位是立方米 (m ³ )。

使用边长的立方体体积

立方体所有边的度量都是相同的，因此我们只需要知道一个边即可计算立方体的体积。使用边长计算立方体体积的步骤是，

• 第 1 步：记下立方体的边长，比如边。
• 第 2 步：现在，立方体的体积 = (side) ³ 。
• 第 3 步：最终答案与立方单位一起测量。

立方体公式的体积

Volume of the cube = Side × Side × Side = Side³

如果立方体的长度增加一倍，它的体积会发生什么变化？

解决方案：

Volume of the cube = Side³

Since,

All the sides of the cube are equal

Then if the length of a side of the cube is increased 

So, the side of the cube becomes

Side of the cube = 2 × Side

Assume

Side of the cube be ‘s’

Side of the cube = 2s

Now,

Volume of the cube = 2s × 2s × 2s

Volume of the cube = (2s)³

Volume of the cube = 8s³

To find how many times the volume of the cube is increased

⇒  $\frac{Volume\ of\ the\ increased\ length\ cube}{Volume\ of\ the\ initial\ cube}$

⇒ 8s³/ s³

⇒ 8

Therefore,

If the length of the cube is doubled then its volume is increased by 8 times.

示例问题

问题1.如果立方体的边减少到一半会发生什么？

解决方案：

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is decreased to half

Therefore,

Side of the cube = s/2

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = s/2 × s/2 × s/2

Volume of the decreased side cube = (s/2)³

Volume of the decreased side cube = s³/8

Therefore,

If we decrease the side of the cube to half then its volume is decreased by 8 times.

问题2.如果立方体的边增加三倍，立方体的体积会增加多少倍？

解决方案：

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is increased by 3 times

Therefore,

Side of the cube = 3 × s

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = 3s × 3s × 3s

Volume of the decreased side cube = (3s)³

Volume of the decreased side cube = 27s³

Therefore,

If we increase the side of the cube to 3 times then its volume is increased by 27 times.

问题3.如果立方体的边减少到1/4，计算立方体体积的减少量？

解决方案：

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Assume the side of the cube be ‘s’

Volume of the cube = s³

According to the question

The side of the cube is decreased to 1/4

Therefore,

Side of the cube = s/4

Now,

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of the decreased side cube = s/4 × s/4 × s/4

Volume of the decreased side cube = (s/4)³

Volume of the decreased side cube = s³/64

Therefore,

If we decrease the side of the cube by 1/4 then its volume decreases by 64 times.

问题 4. 求一个边长为 8 厘米的大立方体可以拼出多少个边长为 2 厘米的小立方体？

解决方案：

As we know that

Volume of the cube = Side × Side × Side

Volume of the cube = Side³

Volume of small cube = 2 × 2 × 2

Volume of small cube = 8 cm³

Volume of big cube = 8 × 8 × 8

Volume of big cube = 512 cm³

To find how many small cubes can be made out of big cube

⇒ $\frac{Volume\ of\ the\ big\ cube}{Volume\ of\ the\ small\ cube}$

⇒ 512/8

⇒ 64

Therefore,

64 small cubes of side 2 cm can be made out of a big cube of side 8 cm.