# What is the formula for determining the mass?

## Exercises Volume and Mass I

First, I will again introduce the formula for calculating the mass of a body:

To calculate the mass of a body we need the density and the volume:

Mass = volume times density.

### 1. Calculate the volume and mass of the complex casting!

Density:

### 2. Calculate the volume and mass of the aluminum part!

Density:

### 3. Calculate the volume and mass of the steel part.

Density:

### 4. Calculate the volume and mass of the copper part!

The material is 12 mm thick.

Density:

### 5. A steel pipe is 10 m long (L = 10 m), has an outside diameter of D = 20 cm and an inside diameter of d = 160 mm.

Calculate that **volume**, the **Dimensions** and the **Wall thickness** of the pipe!

### 1. Detailed solution:

Calculate the volume and mass of the casting.

Density:

All dimensions in the drawing are converted to decimeters (dm).

The following applies for the conversion: 100 mm = 1 dm, 10,000 mm^{2} = 1 dm^{2} and 1,000,000 mm^{3} = 1 dm^{3}

To determine the volume, the area of the workpiece is multiplied by its thickness. The results are to be rounded to three places behind the decimal point.

### 2. Detailed solution:

Calculate the volume and mass of the aluminum part.

Density:

All dimensions in the drawing are converted to decimeters (dm).

The following applies for the conversion: 100 mm = 1 dm, 10,000 mm^{2} = 1 dm^{2} and 1,000,000 mm^{3} = 1 dm^{3}

To determine the volume, the area of the workpiece is multiplied by its thickness. The results are to be rounded to three places behind the decimal point.

#### 3. Detailed solution:

Calculate the volume and mass of the steel part.

Density:

All dimensions in the drawing are converted to decimeters (dm).

The following applies for the conversion: 100 mm = 1 dm, 10,000 mm^{2} = 1 dm^{2} and 1,000,000 mm^{3} = 1 dm^{3}

The results are to be rounded to three places behind the decimal point.

### 4. Detailed solution:

Calculate the volume and mass of the copper part. The material is 12 mm thick.

Density:

All dimensions in the drawing are converted to decimeters (dm).

The following applies for the conversion: 100 mm = 1 dm, 10,000 mm^{2} = 1 dm^{2} and 1,000,000 mm^{3} = 1 dm^{3}

To determine the volume, the area of the workpiece is multiplied by its thickness. The results are to be rounded to three places behind the decimal point.

### 5. Detailed solution:

A steel pipe is 10 m long (L = 10 m), has an outside diameter of D = 20 cm and an inside diameter of d = 160 mm.

Calculate the volume, mass and wall thickness of the pipe.

All dimensions in the drawing are converted to decimeters (dm).

The following applies for the conversion: 100 mm = 1 dm, 10,000 mm^{2} = 1 dm^{2} and 1,000,000 mm^{3} = 1 dm^{3}

The results are to be rounded to three places behind the decimal point.

#### You can find one here **Tables for converting powers of ten, lengths, areas, volumes with exercises and solutions.**

#### And here is an overview of all articles on the subject of geometry, including links to other tasks.

**You can buy these and other teaching materials in our shop. There teachers will find WORD files that they can change as required. You can also download all materials as PFD files for free. **

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