Volume, area and converting units

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What is Volume?

Volume is the amount of space a 3D shape takes up.
Think of a box: volume tells you how much it can hold.
We measure volume in cubic units, like cubic centimetres (cm³).
A unit cube is a cube with sides of 1 unit, like 1 cm. Its volume is 1 cm³.
To find volume, we count how many unit cubes fit inside the shape.

Units of Length, Area, and Volume

Length is measured in units like centimetres (cm) or metres (m).
Area is measured in square units, like square centimetres (cm²).
Volume is measured in cubic units, like cubic centimetres (cm³).
Remember: cm for length, cm² for area, cm³ for volume.
A square with side 1 cm has area 1 cm². A cube with side 1 cm has volume 1 cm³.

Converting Units of Length

To convert between units, use conversion factors.
For length: 1 m = 100 cm, 1 km = 1000 m.
To go from a larger unit to a smaller one, multiply.
Example: 3 m = 3 × 100 = 300 cm.
To go from a smaller unit to a larger one, divide.
Example: 500 cm = 500 ÷ 100 = 5 m.

Converting Units of Area

Area units convert by squaring the length conversion factor.
Since 1 m = 100 cm, then 1 m² = 100 × 100 = 10,000 cm².
To convert from m² to cm², multiply by 10,000.
Example: 2 m² = 2 × 10,000 = 20,000 cm².
To convert from cm² to m², divide by 10,000.
Example: 50,000 cm² = 50,000 ÷ 10,000 = 5 m².

Converting Units of Volume

Volume units convert by cubing the length conversion factor.
Since 1 m = 100 cm, then 1 m³ = 100 × 100 × 100 = 1,000,000 cm³.
To convert from m³ to cm³, multiply by 1,000,000.
Example: 2 m³ = 2 × 1,000,000 = 2,000,000 cm³.
To convert from cm³ to m³, divide by 1,000,000.
Example: 3,000,000 cm³ = 3,000,000 ÷ 1,000,000 = 3 m³.

Finding Volume of a Cuboid

A cuboid is a box shape with 6 rectangular faces.
To find its volume, use the formula: V = l × w × h.
Here, V = volume, l = length, w = width, h = height.
Measure all sides in the same unit, then multiply.
Example: A box with l = 5 cm, w = 3 cm, h = 2 cm has V = 5 × 3 × 2 = 30 cm³.
You can also find volume by multiplying the area of the base by the height.

Volume by Base Area

The base is the bottom face of a cuboid.
The area of the base is length × width.
Then multiply by the height: V = base area × h.
This works because stacking base layers fills the height.
Example: If base area = 12 cm² and h = 4 cm, then V = 12 × 4 = 48 cm³.

Adding Volumes of Combined Shapes

Sometimes a solid is made of two cuboids stuck together.
Find the volume of each cuboid separately.
Then add the volumes to get the total volume.
Example: Cuboid A has volume 20 cm³, cuboid B has volume 15 cm³, total = 35 cm³.
Make sure to use the same unit for both volumes.

Area vs Perimeter vs Volume

Perimeter is the distance around a 2D shape. Measured in units like cm.
Area is the space inside a 2D shape. Measured in square units like cm².
Volume is the space inside a 3D shape. Measured in cubic units like cm³.
Perimeter is for 2D shapes only; area is for 2D shapes; volume is for 3D shapes.
Example: A rectangle has perimeter = 2 × (length + width), area = length × width. A box has volume = length × width × height.

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Câu hỏi luyện tập

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1.What is volume?
Easy
- AThe amount of space a 3D shape takes up
- BThe distance around a shape
- CThe amount of surface a shape covers
- DThe weight of an object
2.Which unit is used for volume?
Easy
- Acm
- Bcm2
- Ccm3
- Dg
3.Area is measured in square units, like cm2.
Easy
True or false?
4.A cuboid has length 5 cm, width 3 cm, and height 2 cm. What is its volume?
Easy
- A10 cm3
- B15 cm3
- C30 cm3
- D60 cm3
5.Which of the following are correct statements about units? (select all that apply)
Medium
- A1 m = 100 cm
- B1 m2 = 100 cm2
- C1 m3 = 1000 cm3
- D1 L = 1000 mL
- E1 cm3 = 1 mL
6.Put these units in order from smallest to largest volume.
Medium
- 1 cm3
- 1 mL
- 1 L
- 1 m3
7.Match each measurement to the correct unit.
Medium
- Length
- Area
- Volume
- cm
- cm2
- cm3
8.Which of these are correct conversions? (select all that apply)
Medium
- A1 L = 1000 mL
- B1 m = 100 cm
- C1 cm³ = 1 mL
- D1 m³ = 1000 cm³

Thêm câu hỏi

9.Volume is measured in square units.
Easy
True or false?
10.A rectangular prism has a volume of 150 cm³. Its length is 5 cm and its width is 5 cm. What is its height?
Medium
- A6 cm
- B30 cm
- C10 cm
- D3 cm
11.Which of these has the greatest volume?
Medium
- AA cube with side 2 cm
- BA cuboid 3 cm by 2 cm by 2 cm
- CA cuboid 4 cm by 1 cm by 2 cm
- DA cube with side 1.5 cm
12.Which of these statements about volume are true? (select all that apply)
Medium
- AVolume is the amount of space a 3D shape takes up.
- BVolume can be measured by counting unit cubes.
- CVolume is measured in square units.
- DThe volume of a cuboid is length × width × height.
13.A cube has side length 5 cm. What is its volume?
Medium
- A25 cm³
- B15 cm³
- C125 cm³
- D50 cm³
14.A rectangular prism has a volume of 96 cm³. Its length is 4 cm and its width is 3 cm. What is its height?
Medium
- A8 cm
- B6 cm
- C12 cm
- D4 cm
15.To find the volume of a cuboid, you multiply its length, width, and height.
Easy
True or false?
16.A shape is made by joining two cuboids. Cuboid A is 6 cm long, 2 cm wide, and 2 cm high. Cuboid B is 4 cm long, 2 cm wide, and 2 cm high. What is the total volume of the shape?
Medium
- A40 cm³
- B32 cm³
- C48 cm³
- D24 cm³
17.Which of the following is the correct conversion?
Medium
- A1 m³ = 100 cm³
- B1 m³ = 1000 cm³
- C1 m³ = 1,000,000 cm³
- D1 m³ = 10,000 cm³
18.Which of the following are correct statements about volume? (select all that apply)
Medium
- AVolume is measured in cubic units.
- BVolume is the amount of space a 3D shape takes up.
- CVolume can be measured in square units.
- DTo find the volume of a cuboid, multiply length by width by height.
19.Put these volumes in order from smallest to largest.
Medium
- 1 L
- 500 mL
- 2 L
20.A box has a base area of 24 cm² and a height of 5 cm. What is its volume?
Medium
- A120 cm³
- B29 cm³
- C100 cm³
- D120 cm²
21.Which of the following are correct conversions? (Select all that apply)
Medium
- A2.5 L = 2500 mL
- B0.75 m³ = 750,000 cm³
- C3.2 L = 320 cm³
- D1 cm³ = 0.001 L
22.To find the volume of a cuboid, you can multiply the area of its base by its height.
Easy
True or false?
23.A cube has a side length of 6 cm. What is its volume?
Medium
- A18 cm³
- B36 cm³
- C216 cm³
- D216 cm²
24.1 cubic metre (m³) is equal to 1000 litres.
Easy
True or false?
25.A water tank is 1.5 m long, 0.8 m wide, and 0.6 m high. How many litres of water does it hold when full? (1 m³ = 1000 L)
Hard
- A720 L
- B72 L
- C7200 L
- D7.2 L
26.What does the volume of an object measure?
Easy
- AThe amount of space it takes up
- BThe length of its sides
- CThe weight of the object
- DThe area of its surface
27.A two-dimensional shape, like a square, has volume.
Easy
True or false?
28.Which of the following is the correct unit for volume?
Easy
- Acm²
- Bcm³
- Ccm
- Dlitres per metre
29.Match each measurement with the correct unit.
Easy
- Length
- Area
- Volume
- cm
- cm²
- cm³
30.A cuboid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its volume?
Medium
- A120 cm³
- B16 cm³
- C40 cm³
- D125 cm³
31.A cube has a side length of 4 cm. What is its volume?
Medium
- A64 cm³
- B16 cm³
- C12 cm³
- D8 cm³
32.The volume of a 2D shape like a square is zero.
Easy
True or false?
33.A cuboid has a base area of 20 cm² and a height of 4 cm. What is its volume?
Medium
- A80 cm³
- B16 cm³
- C24 cm³
- D5 cm³
34.A fish tank is 50 cm long, 30 cm wide, and 40 cm high. How many litres of water can it hold? (1 L = 1000 cm³)
Medium
- A60 L
- B600 L
- C6 L
- D60000 L
35.Put these measurements in order from smallest to largest.
Medium
- 2 L
- 1500 mL
- 0.002 m³
- 200 cm³
36.A box is 1.2 m long, 0.8 m wide, and 0.5 m high. What is its volume in cubic centimetres?
Hard
- A480000 cm³
- B4800 cm³
- C480 cm³
- D48 cm³
37.Which unit is used to measure volume?
Easy
- Acm
- Bcm²
- Ccm³
- Dkg
38.What is the volume of a cuboid with length 4 cm, width 3 cm, and height 2 cm?
Easy
- A9 cm³
- B24 cm³
- C12 cm³
- D20 cm³
39.Area is measured in square units like cm².
Easy
True or false?
40.A cuboid has a volume of 240 cm³. Its base area is 40 cm². What is its height in centimetres?
Medium
- A6 cm
- B8 cm
- C10 cm
- D4 cm
41.A cube has side length 4 cm. What is its volume in cubic centimetres?
Easy
42.Complete the sentences.
Easy
To find the volume of a cuboid, multiply its ____ by its ____ by its ____.
43.What is the volume of a cuboid with a base area of 12 cm2 and a height of 5 cm? Write your answer with the correct unit.
Medium
44.A rectangular prism has a volume of 120 cm3. Its length is 5 cm and its width is 4 cm. What is its height in cm?
Medium
45.A cuboid has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is its volume in cubic centimetres?
Medium
46.A rectangular prism has a volume of 240 cm³. Its base area is 40 cm². What is its height in centimetres?
Medium
47.A shape is made by joining two cuboids. Cuboid A is 5 cm long, 2 cm wide, and 3 cm high. Cuboid B is 4 cm long, 2 cm wide, and 2 cm high. What is the total volume of the shape in cubic centimetres?
Hard
48.What is the volume of a cube with side length 3 cm? Write your answer as a number and unit.
Easy
49.Complete the conversion.
Medium
2.5 L = ____ mL
50.A cuboid has a length of 7 cm, a width of 2 cm, and a height of 3 cm. What is its volume in cubic centimetres?
Easy
51.A cuboid has a base area of 18 cm² and a height of 4 cm. What is its volume in cubic centimetres?
Medium
52.Fill in the missing number.
Easy
1 litre = ____ millilitres.
53.Explain how to find the volume of a shape made from two cuboids joined together.
Hard
54.Explain how to convert 2.5 litres to millilitres.
Hard
55.A rectangular prism has a volume of 150 cm³. Its length is 5 cm and its width is 5 cm. What is its height? Explain your method.
Hard
56.Explain how to find the volume of a shape made from two cuboids joined together. Use an example.
Hard
57.Explain how to convert 2.5 litres to millilitres. Show your working.
Medium
58.A cube has side length 4 cm. What is its volume in cubic centimetres?
Easy
- A70 cm3
- B58 cm3
- C64 cm3
- D76 cm3
59.A rectangular prism has a volume of 120 cm3. Its length is 5 cm and its width is 4 cm. What is its height in cm?
Medium
- A6 cm
- B8 cm
- C5 cm
- D7 cm
60.A cuboid has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is its volume in cubic centimetres?
Medium
- A79 cm³
- B72 cm³
- C65 cm³
- D86 cm³
61.A rectangular prism has a volume of 240 cm³. Its base area is 40 cm². What is its height in centimetres?
Medium
- A6 cm
- B5 cm
- C8 cm
- D7 cm
62.A shape is made by joining two cuboids. Cuboid A is 5 cm long, 2 cm wide, and 3 cm high. Cuboid B is 4 cm long, 2 cm wide, and 2 cm high. What is the total volume of the shape in cubic centimetres?
Hard
- A41 cm³
- B51 cm³
- C56 cm³
- D46 cm³
63.A cuboid has a length of 7 cm, a width of 2 cm, and a height of 3 cm. What is its volume in cubic centimetres?
Easy
- A42 cm³
- B46 cm³
- C50 cm³
- D38 cm³
64.A cuboid has a base area of 18 cm² and a height of 4 cm. What is its volume in cubic centimetres?
Medium
- A65 cm³
- B86 cm³
- C72 cm³
- D79 cm³

Ghi chú ôn tập

## Volume, Area, and Converting Units ### What is Volume? Volume is how much space a 3D shape takes up. Think of it as the number of unit cubes (like sugar cubes) that fit inside. Unit cubes have sides of length 1 unit (like 1 cm). ### Units of Measurement - **Length** is measured in units like **cm** (centimetres), **m** (metres), or **km** (kilometres). - **Area** (the space inside a flat shape) is measured in square units like **cm²** (square centimetres) or **m²**. - **Volume** is measured in cubic units like **cm³** (cubic centimetres) or **m³**. **Remember:** - Use **cm** for length, **cm²** for area, **cm³** for volume. ### Converting Units You can change from one unit to another within the same system (like metric). For example: - 1 m = 100 cm - 1 m² = 100 cm × 100 cm = 10,000 cm² - 1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³ To convert, multiply or divide by the right number. For example, to change 2 m to cm: 2 × 100 = 200 cm. ### Finding Volume of a Cuboid A cuboid is a box shape with length, width, and height. **Formula:** Volume = length × width × height Or you can find the area of the base (length × width) and multiply by the height. **Example:** A box is 5 cm long, 3 cm wide, and 4 cm high. Volume = 5 × 3 × 4 = 60 cm³ ### Adding Volumes If a solid is made of two cuboids, find the volume of each part and add them together. **Example:** A shape has one part with volume 20 cm³ and another with volume 30 cm³. Total volume = 20 + 30 = 50 cm³. ### Area vs Perimeter vs Volume - **Perimeter** is the distance around a flat shape (in cm, m). - **Area** is the space inside a flat shape (in cm², m²). - **Volume** is the space inside a 3D shape (in cm³, m³). Don't mix them up!

Volume: The amount of space a 3D shape takes up, measured in cubic units like cm³.
Area: The amount of space inside a flat (2D) shape, measured in square units like cm².
Perimeter: The total distance around the outside of a flat shape, measured in units like cm.
Cuboid: A 3D box shape with six rectangular faces. Its volume is length × width × height.
Unit cube: A cube with sides of length 1 unit, used to measure volume by counting how many fit inside a shape.
Convert: To change a measurement from one unit to another, like from metres to centimetres.
cm³: Cubic centimetre, a unit of volume. It is the space a cube with sides of 1 cm takes up.
m³: Cubic metre, a unit of volume. It is the space a cube with sides of 1 m takes up.

Thẻ ghi nhớ

What is volume?

Volume is the amount of space a 3D shape takes up. We measure it in cubic units like cm³.

What is area?

Area is the amount of surface a 2D shape covers. We measure it in square units like cm².

What is perimeter?

Perimeter is the distance around a 2D shape. We measure it in units like cm.

Which unit is used for volume: cm, cm², or cm³?

cm³ (cubic centimetres) is used for volume. cm is for length, cm² is for area.

How do you find the volume of a cuboid?

Multiply length × width × height. Example: 3 cm × 2 cm × 4 cm = 24 cm³.

How do you find the volume of a cuboid using its base area?

Multiply the area of the base by the height: Volume = base area × height.

A cuboid has a base area of 12 cm² and a height of 5 cm. What is its volume?

Volume = 12 cm² × 5 cm = 60 cm³.

How do you find the volume of a solid made of two cuboids?

Find the volume of each cuboid separately, then add them together.

A solid is made of a 2 cm × 3 cm × 4 cm cuboid and a 1 cm × 1 cm × 1 cm cube. What is its total volume?

First cuboid: 2×3×4 = 24 cm³. Cube: 1×1×1 = 1 cm³. Total = 24 + 1 = 25 cm³.

What is a unit cube?

A cube with side length 1 unit. Its volume is 1 cubic unit (like 1 cm³).

How do you measure volume by counting unit cubes?

Count how many unit cubes fit inside the shape. The number of cubes is the volume in cubic units.

How many unit cubes are in a 2 cm × 3 cm × 4 cm cuboid?

You can count: 2 × 3 × 4 = 24 unit cubes, so volume is 24 cm³.

How many millilitres (mL) are in 1 litre (L)?

1 L = 1000 mL.

How many centimetres (cm) are in 1 metre (m)?

1 m = 100 cm.

How many square centimetres (cm²) are in 1 square metre (m²)?

1 m² = 10,000 cm². Because 1 m = 100 cm, so 100 × 100 = 10,000.

How many cubic centimetres (cm³) are in 1 cubic metre (m³)?

1 m³ = 1,000,000 cm³. Because 1 m = 100 cm, so 100 × 100 × 100 = 1,000,000.

How many millilitres (mL) are in 1 cubic centimetre (cm³)?

1 mL = 1 cm³. They are the same volume.

How many litres (L) are in 1 cubic metre (m³)?

1 m³ = 1000 L. Because 1 m³ = 1,000,000 cm³ and 1 L = 1000 cm³, so 1,000,000 ÷ 1000 = 1000.

Convert 3.5 L to millilitres.

3.5 L = 3500 mL. Because 1 L = 1000 mL, so 3.5 × 1000 = 3500.

Convert 2500 cm³ to litres.

2500 cm³ = 2.5 L. Because 1000 cm³ = 1 L, so 2500 ÷ 1000 = 2.5.

A rectangular box is 10 cm long, 5 cm wide, and 2 cm high. What is its volume?

Volume = 10 × 5 × 2 = 100 cm³.

A cuboid has a volume of 60 cm³. Its base area is 15 cm². What is its height?

Height = Volume ÷ base area = 60 ÷ 15 = 4 cm.

What is the difference between area and volume?

Area is for flat 2D shapes (like a square), measured in square units. Volume is for solid 3D shapes (like a box), measured in cubic units.

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