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Common Core for Grade 7

Common Core for Mathematics

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Common Core: 7.G.6

### Suggested Learning Targets

**Area, Volume and Surface Area 1 (7.G.6)**

Area Review

Definition: Volume is the amount of space a 3-dimensional figure takes up.

Strategy: With many shapes, you can calculate volume by multiplying the area of the base by the height.

Definition: Surface area is the area of all the surfaces of a 3-dimensional figure.

Strategy: Visualize the surface area by making "nets" that "unfold" the shape.
### Volume

Volume of Cubes and Rectangular Prisms

**Volume of a Triangular Prism (A Tent Shaped Object)**

Finding the volume of a prism

**Volume Story Problem - Capacity And Cost**

Example:

A swimming pool with dimensions shown below is filled two-thirds of the way. If the cost to fill the pool is $0.04 per cubit ft of water, how much did it cost to fill the pool two-thirds of the way?

**Volume Word Problem Example**

Example:

A water tank is 12 feet high, 5 feet long, and 9 feet wide. A solid metal box which is 7 feet high, 4 feet long and 5 feet wide is sitting at the bottom of the tank. What is the volume of the water in the tank?

### Surface Area

Rectangular Prisms - Volume and Surface Area

Using a net

**Right Triangular Prism - Volume and Surface Area**

**Trapezoidal Prisms - Volume and Surface Area**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core for Grade 7

Common Core for Mathematics

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Common Core: 7.G.6

- I can solve mathematical problems involving the area of triangles, quadrilaterals, and other polygons.
- I can solve mathematical problems involving the volume and surface area of cubes and right prisms.
- I can solve real-world problems involving the area of triangles, quadrilaterals, and other polygons.
- I cam solve real-world problems involving the volume and surface area of cubes and right prisms.
- I can solve mathematical and real-world problems
involving the area, circumference, surface
area, and volume of composite objects (2D & 3D)

Area Review

Definition: Volume is the amount of space a 3-dimensional figure takes up.

Strategy: With many shapes, you can calculate volume by multiplying the area of the base by the height.

Definition: Surface area is the area of all the surfaces of a 3-dimensional figure.

Strategy: Visualize the surface area by making "nets" that "unfold" the shape.

Finding the volume of a prism

Example:

A swimming pool with dimensions shown below is filled two-thirds of the way. If the cost to fill the pool is $0.04 per cubit ft of water, how much did it cost to fill the pool two-thirds of the way?

Example:

A water tank is 12 feet high, 5 feet long, and 9 feet wide. A solid metal box which is 7 feet high, 4 feet long and 5 feet wide is sitting at the bottom of the tank. What is the volume of the water in the tank?

Using a net

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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