# 6.3.4. Volume of a Cuboid

The perimeter of the base of a cuboid is cm. If the ratio between the length and width of its base is , where the height of the cuboid is cm, calculate its volume.

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### Example

The perimeter of the base of a cuboid is cm. The ratio between the length and width of its base is . If the height of the cuboid is cm, calculate its volume.

### Solution

Step 1: Find the sum of the length width.

Since the perimeter of a cuboid's base = 2 (length + width), we know that length + width = perimeter 2.

Step 2: Find the base's length and the base's width.

We can use the concept of "the sum of parts." The ratio of the base's length to its width is . So, the length = 5 parts, and the width = 4 parts.

The sum of the length width = 5 parts 4 parts = 9 parts.

Since 9 parts = cm, then one part = 18 9 = cm. We can use the value of one part to find the base's length and to find the base's width.

Step 3: Find the volume.

Use the formula for the volume of a cuboid.

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