# Difference Between Area and Volume

#### Grade 7 Math Worksheets

**Area is the measure of the space covered by a flat surface, while volume is the measure of the amount of space occupied by a solid object or region.**

Table of Contents:

- What is Area?
- What is Volume?
- Difference Between Area and Volume
- Formulas for calculating the area of various shapes
- FAQs

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## Difference Between Area and Volume - Grade 7 Math Worksheet PDF

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## Difference Between Area and Volume

The key difference between area and volume is that area is the measure of the space covered by a flat surface, while volume is the measure of the amount of space occupied by a solid object or region. Area is two-dimensional and measures the size of a surface, while volume is three-dimensional and measures the capacity or space inside an object.

### What is Area?

Area measures how much space is covered or enclosed by a flat surface or shape. It tells us the size of a surface or the amount of space it occupies.

For example, if you have a rectangular garden, the area would tell you how much ground it covers. It is usually expressed in square units such as square meters or square feet. So, in essence, area helps us understand the extent or size of a two-dimensional surface.

### What is Volume?

Volume is the measure of how much space an object or region occupies in three dimensions. It tells us the capacity or amount of space inside a solid object.

For example, if you have a box, the volume would tell you how much it can hold. It is usually expressed in cubic units such as cubic meters or cubic feet. So, volume helps us understand the amount of space that a three-dimensional object takes up or the space contained within a specific region.

### What is the difference between Area and Volume?

#### Area:

- Area is a two-dimensional measurement.
- It represents the amount of space covered by a flat surface.
- It is measured in square units such as square meters or square feet.
- Area quantifies the size or extent of a surface.
- It helps determine the amount of space enclosed within the boundary of a two-dimensional shape or surface.

#### Volume:

- Volume is a three-dimensional measurement.
- It represents the amount of space occupied by a solid object or contained within a three-dimensional region.
- It is measured in cubic units such as cubic meters or cubic feet.
- Volume quantifies the capacity or amount of space within a three-dimensional object.
- It helps determine the space enclosed within the boundary of a solid shape.

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## Formulas for Calculating the Area of Various Shapes:

**1. Rectangle:**

Area = length × width

**2. Square:**

Area = side length × side length

3. Triangle:

**Area = 0.5 × base × height**

**4. Circle:**

Area = π × radius²

**4. Parallelogram:**

Area = base × height

**5. Trapezoid:**

Area = 0.5 × (base1 + base2) × height

**6. Ellipse:**

Area = π × major axis length × minor axis length

**7. Regular Polygon:**

Area = (perimeter × apothem) / 2

## Formulas for Calculating the Volume of Various Shapes:

**1. Cube:**

Volume = side length × side length × side length

**2. Rectangular Prism (or Cuboid):**

Volume = length × width × height

**3. Cylinder:**

Volume = π × radius² × height

**4. Sphere:**

Volume = (4/3) × π × radius³

**5. Cone:**

Volume = (1/3) × π × radius² × height

**6. Pyramid:**

Volume = (1/3) × base area × height

**7. Triangular Prism:**

Volume = (1/2) × base × height × length

**8. Ellipsoid:**

Volume = (4/3) × π × radius1 × radius2 × radius3

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## Difference Between Area and Volume FAQS

##### What is the primary difference between area and volume?

The main difference is that area measures the size or extent of a two-dimensional surface, while volume measures the capacity or amount of space occupied by a three-dimensional object or region.

##### How are area and volume measured?

Area is measured in square units, such as square meters (m²) or square inches (in²), while volume is measured in cubic units, such as cubic meters (m³) or cubic inches (in³).

##### What does the area represent?

Area represents the amount of space covered by a flat surface or shape. It quantifies the size or extent of a two-dimensional region.

##### What does volume represent?

Volume represents the amount of space occupied by a solid object or contained within a three-dimensional region. It quantifies the capacity or space inside a three-dimensional shape.

##### Are area and volume dimensions the same?

No, they are different. Area is a two-dimensional measurement, while volume is a three-dimensional measurement.

**Gloria Mathew** writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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