Area and Volume Worksheet — KS3 — Intermediate

Area and Volume worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Area and Volumeintermediate

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Exploring Area and Volume

Key Stage 3 / Year 7-9 (Ages 11-14) - Intermediate

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Instructions: This worksheet will help you understand and calculate the area and volume of various shapes. Follow the instructions for each activity carefully, and use the provided spaces to write your answers.

Calculating the Area of Rectangles

Calculate the area of each rectangle using the formula Area = length × width. Write your answer in the space provided.

1. Length = 5 cm, Width = 3 cm

2. Length = 7 cm, Width = 4 cm

3. Length = 8 cm, Width = 6 cm

4. Length = 10 cm, Width = 2 cm

Volume of Cubes

Calculate the volume of each cube using the formula Volume = side³. Write your answer in the space provided.

1. Side = 3 cm

2. Side = 5 cm

3. Side = 7 cm

4. Side = 4 cm

Area of Triangles

Use the formula Area = 0.5 × base × height to find the area of each triangle. Write your answer in the space provided.

1. Base = 6 cm, Height = 4 cm

2. Base = 8 cm, Height = 5 cm

3. Base = 10 cm, Height = 7 cm

4. Base = 12 cm, Height = 9 cm

Volume of Rectangular Prisms

Calculate the volume of each rectangular prism using the formula Volume = length × width × height. Write your answer in the space provided.

1. Length = 4 cm, Width = 3 cm, Height = 2 cm

2. Length = 6 cm, Width = 5 cm, Height = 4 cm

3. Length = 8 cm, Width = 7 cm, Height = 6 cm

4. Length = 10 cm, Width = 9 cm, Height = 8 cm

Understanding Surface Area

Calculate the surface area of each cube using the formula Surface Area = 6 × side². Write your answer in the space provided.

1. Side = 2 cm

2. Side = 4 cm

3. Side = 6 cm

4. Side = 8 cm

Comparing Areas

Compare the areas of the given shapes and determine which one is larger. Write 'Shape 1' or 'Shape 2' in the space provided.

1. Shape 1: Length = 5 cm, Width = 4 cm; Shape 2: Length = 6 cm, Width = 3 cm

2. Shape 1: Base = 10 cm, Height = 5 cm; Shape 2: Base = 8 cm, Height = 7 cm

Volume Word Problems

Read each word problem carefully and calculate the volume of the object described. Write your answer in the space provided.

1. A box has a length of 10 cm, a width of 5 cm, and a height of 4 cm. What is its volume?

2. A swimming pool is 20 m long, 10 m wide, and 2 m deep. What is its volume?

Area and Volume Challenge

Solve these challenging problems involving both area and volume. Show all your workings and write your answers in the space provided.

1. Calculate the area of a rectangle with a length of 12 cm and a width of 8 cm, then find the volume if the rectangle is extruded to form a prism with a height of 5 cm.

2. A triangular prism has a base triangle with a base of 6 cm and a height of 4 cm. If the height of the prism is 10 cm, what is its volume?

Answer Key

Activity 1: 15 cm² ; 28 cm² ; 48 cm² ; 20 cm²

Activity 2: 27 cm³ ; 125 cm³ ; 343 cm³ ; 64 cm³

Activity 3: 12 cm² ; 20 cm² ; 35 cm² ; 54 cm²

Activity 4: 24 cm³ ; 120 cm³ ; 336 cm³ ; 720 cm³

Activity 5: 24 cm² ; 96 cm² ; 216 cm² ; 384 cm²

Activity 6: Shape 1 ; Shape 2

Activity 7: 200 cm³ ; 400 m³

Activity 8: 96 cm², 480 cm³ ; 120 cm³