• SkillCat Team

HVAC Trade Math: Geometry

Updated: Jul 1

HVAC Trade Math: Chapter 2


Geometry


In this module, we will talk about different shapes and how to find their area, perimeter, and volume. Skip to quiz!


Overview


Two-dimensional shapes are formed on a flat surface. 2D shapes have two dimensions: length and width. They have no depth.


For example, anything we draw or write on a piece of paper is two-dimensional. This is because the paper is entirely flat.


Two-dimensional shapes are all around us. Some examples of 2D shapes include square, rectangle, circle, and triangle.


3D shapes have three dimensions: length, width, and thickness. Examples of 3D shapes include cube, cone, sphere, etc.


3D shapes are everywhere. A dice is an example of a cube.An ice cream cone is an example of cone. A soccer ball is an example of a sphere.



Area


Area is the amount of space a shape takes up on a flat surface. 2D shapes have two dimensions: length and width. This is why area is calculated using squared units such as cm² and m².


To find the area of any shape, all we need is the length and the width. Let’s take a look at how we can find the area of shapes such as square, rectangle, and triangle.



Perimeter


Perimeter is the total length of all the sides of a 2D shape. To calculate the perimeter of any shape, we add up the length of each side. Let us look at how to calculate the perimeter of a square, rectangle, and triangle.



Volume


Volume is the space a three-dimensional shape takes up. 3D shapes have three dimensions: length, width, and thickness. Volume is calculated in cubic units such as cm³ and m³.


Similar to calculating area and perimeter, different equations are used to calculate the volume of different shapes. Let’s take a look at how we can find the volume of shapes such as cube, cone, and sphere.



Circles


A circle is a round shape that has no corners. The distance from the center of a circle to any point on the edge of a circle is the same. This distance is called the radius. The distance from one side of the circle to another is called the diameter.


2D shapes have length and width. A triangle, a square, a rectangle are all 2D shapes. A circle is a 2D shape with no corners.


3D shapes have length, width, and thickness. Cubes, cones, and spheres are examples of 3D shapes.





Question #1: Two dimensional objects only have length and width.

  1. True

  2. False

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Answer: True

Two-dimensional objects are flat; therefore, they have no thickness, only length and width.


Question #2: 3 dimensional objects have length, width, and thickness.

  1. True

  2. False

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Answer: True

3D shapes have three dimensions: length, width, and thickness.


Question #3: What unit is area calculated in?

  1. Squared unit

  2. Cubic unit

  3. No unit

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Answer: Squared unit.

Two-dimensional objects are flat; therefore, they have no thickness, only width and length.


Question #4: What is the area of a square that has a length and width of 2 inches?

  1. 4 in²

  2. 5 in²

  3. 6 in²

  4. 8 in²

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Answer: 4 in²

Use the equation A = s x s to calculate the area of the square.

A = 2 x 2

= 4


Question #5: What is the area of a rectangle that has a length of 2 meter and a width of 3m ?

  1. 6 m

  2. 5

  3. 6 m²

  4. 2 m²

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Answer: 6 m²

Use the equation A = l x w to calculate the area of the rectangle.

A = 2 x 3

= 6


Question #6: What is the area of a triangle that has a height 4 feet and base of 2 feet?

  1. 8 ft²

  2. 6 ft²

  3. 4 ft²

  4. 2 ft²

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Answer: 4 ft²

Use the equation A = ½ (b x h) to calculate the area of the triangle.

A = ½ (4 x 2)

= ½ (8)

= 4


Question #7: What is the perimeter?

  1. The space a shape takes up.

  2. The total length of the shape

  3. None of the above.

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Answer: The total length of the shape

Perimeter is the total length of the shape when all the sides are added up.


Question #8: Find the perimeter of a square with a length of 2 inches.

  1. 8 in

  2. 4 in

  3. 6 in

  4. 2 in

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Answer: 8 in

Use the formula

P = 4 x a to calculate the perimeter of a square.

P = 4 x 2

= 8


Question #9: Find the perimeter of a rectangle with a length of 2 inches and width of 3 inches.

  1. 10 in

  2. 6 in

  3. 4 in

  4. 5 in

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Answer: 10 in

Use the formula

P = 2 x (w + h) to calculate the perimeter of a rectangle.


P = 2 x (2 + 3)

= 2 x 5

= 10


Question #10: Find the perimeter of a triangle that has a length of 3 inches on all three sides.

  1. 9 in

  2. 6 in

  3. 3 in

  4. 4 in

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Answer: 9 in

Use the formula

P = a + b + c to calculate the perimeter of a triangle.


P = 3 + 3 +3

= 9


Question #11: What unit is volume calculated in.

  1. Squared unit

  2. Cubic unit

  3. No unit

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Answer: Cubic unit

Volume is three-dimensional. In 3D, a shape has length, width, and thickness.


Question #12: Find the volume of a cube whose sides are 2 inches.

  1. 8 in³

  2. 8 in

  3. 4 in³

  4. 4 in

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Answer: 8 in³

Use the equation V = S³ to calculate the volume of a cube.


V = 2³

= 8


Question #13: Find the volume of a cone that has a radius of 1 and a height of 2.

  1. 2.09 in³

  2. 1.09 in

  3. 2.0 in³

  4. 3.0 in³

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Answer: 2.09 in³

Use the equation

V = ⅓ ( r² x h) x π.

to calculate the volume of a cone. Remember, π = 3.14


V = ⅓ (1² X 2) x π


= ⅓ (2) x π


= ⅔ x π


= 2.09


Question #14: Find the volume of a sphere with a radius of 3 inches.

  1. 113.1 in³

  2. 1.19 in

  3. 1.19 in³

  4. 2.78 in³

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Answer: 113.1 in³

Use the equation

V = 4/3 (π x r³)

to calculate the volume of a sphere. Remember π = 3.14.


V = 4/3 (π x 3³)

= 4/3 (27π)


= 113.1 in³

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