如何求长方体的体积？

长方体是一种三维形状，其特征是三个维度，即长、宽和高。长方体有六个面，称为面。长方体的每个面都是一个矩形，长方体的所有顶点都包含在直角中。

长方体的属性

长方体具有以下特性：

• 一个长方体有 6 个面、8 个顶点和 12 条边。
• 所有的角度都是直角。
• 所有的脸都是长方形的。
• 每个面包含两条对角线。
• 长方体的相对边缘彼此平行。
• 长方体的尺寸是长、宽和高。

长方体的体积

长方体的体积可以被认为是长方体中所占空间的量度。一个长方体由以下三个维度来标识，即长、宽、高。长方体的体积单位为 (unit) ³ 。

长方体公式的体积

让我们假设一张矩形纸的面积为“A”，它们堆叠的高度为“h”。除此之外，让我们假设长方体的体积为“V”。然后，长方体的体积通过底面积和高度的乘积得到。

The volume of cuboid = Base area × Height

长方体的底面积 = l × b

Hence, the volume of a cuboid, V = l × b × h = lbh

求长方体体积的步骤：

Step 1: All the dimensions of the cuboid are converted to a similar set to achieve consistency.

Step 2: The product of the length, breadth, and height of the cuboid is obtained.

Step 3: The unit is appended to the product.

示例问题

问题 1. 求长 = 50 厘米，宽 = 30 厘米，高 = 15 厘米的长方体的体积？

解决方案：

Here we have to find the volume of the cuboid with the given dimensions

Given:

Length (l) = 50 cm

Breadth (b) = 30 cm

Height (h) = 15 cm

As we know that,

Volume of cuboid = Length × Breadth × Height

Volume of cuboid = l × b × h

Volume of cuboid = 50 × 30 × 15

Volume of cuboid = 22500 cm³

Therefore,

Volume of the cuboid with length = 50 cm, breadth = 30 cm, height = 15 cm is 22500 cm³.

问题2.计算立方仓库的体积，有以下尺寸；

长度 = 30 m

宽度 = 15 m

高度 = 10 m

解决方案：

Here we have to find the volume of the cuboidal warehouse with the given dimensions

Given:

Length (l) = 30 m

Breadth (b) = 15 m

Height (h) = 10 m

As we know that,

Volume of cuboid = Length × Breadth × Height

Volume of cuboidal warehouse = l × b × h

Volume of cuboidal warehouse = 30 × 15 × 10

Volume of cuboid = 4500 m³

Therefore,

Volume of the cuboidal warehouse with length = 30 m, breadth = 15 m, height = 10 m is 4500 m³.

问题 3. 求长方体的长为 750 cm ³ ，宽为 10 cm，高为 5 cm？

解决方案：

Here we have to find the length (l) of the cuboid 

Given:

Volume of cuboid = 750 cm³

Breadth (b) = 10 cm

Height (h)  = 5 cm

As we know that

Volume of cuboid = Length × Breadth × Height

Volume of cuboid = l × b × h

⇒ 750 = l × 10 × 5

⇒ 750 = l × 50

⇒ l = $\frac{750}{50}$

⇒ l = 15 cm

Therefore,

Length of cuboid is 15 cm.

问题 4. 当长方体的长度是高的 4 倍，宽是高的 2 倍时，求长方体的体积。长方体的高度是10 m？

解决方案：

Here we have to find the volume of the cuboid

Given:

Height (h) = 10 m

Length (l) = 4 × h = 4 × 10 = 40 m

Breadth (b) = 2 × h = 2 × 10 = 20 m

Now,

As we know that,

Volume of cuboid = Length × Breadth × Height

Volume of cuboid = l × b × h

Volume of cuboid = 40 × 20 × 10

Volume of cuboid = 8000 m³

Therefore,

Volume of cuboid is 8000 m³.

问题 5. 计算一个长 = 100 厘米，宽 = 50 厘米，高 = 25 厘米的长方体盒子里能装多少空气？

解决方案：

Here we have to find the amount of air that can be filled in the cuboidal box.

Air that can be filled in the cuboidal box = Volume of the cuboidal box

Given:

Length (l) = 100 cm

Breadth (b) = 50 cm

Height (h) = 25 cm

As we know that,

Volume of cuboid = Length × Breadth × Height

Volume of cuboidal box = l × b × h

Volume of cuboidal box = 100 × 50 × 25

Volume of cuboidal box = 125000 cm³

Therefore,

The amount of air that can be filled in a cuboidal box is 125000 cm³.