Volume, Surface Area, and Manipulating Equations

Volume, Surface Area, and Manipulating Equations

Mini Lesson

Multiple Choice

This Shape is a:

• Sphere

• Prism

• Cylinder

• Pyramid

Multiple Choice

This Shape is a:

• Sphere

• Prism

• Cylinder

• Pyramid

Multiple Choice

This Shape is a:

• Sphere

• Prism

• Cylinder

• Pyramid

Multiple Choice

This Shape is a:

• Sphere

• Prism

• Cylinder

• Pyramid

Volume of 3D Shapes

• Volume is the measurement or quantity that a 3D shape occupies or contains (how much space it takes up or how much room is inside it)

• Every shape has it's own Volume formula, where all you have to do is plug in the given information to calculate the volume.

• There are also times where you will have to rearrange the formula to make it work based on the information you are given.

• Volume is measured in cubed units because it is a 3D shape. Cubed=3 sides (Ex: 240 m³ , 3.5 in³ )

Surface Area of 3D Shapes

• Surface Area is the sum of all the areas of the faces (flat sides) of a 3D shape

• Every shape has it's own Surface Area formula, where all you have to do is plug in the given information to calculate the surface areas.

• There are also times where you will have to rearrange the formula to make it work based on the information you are given.

• Think of Surface Area as how much wrapping paper you would need to cover the outside of the shape.

Multiple Choice

What is volume?

• The total amount of space inside of a 3d shape

• The total amount of space on the outside of a 3d shape

Multiple Choice

What is Surface Area?

• The total amount of space inside of a 3d shape

• The total amount of space on the outside of a 3d shape

Now you are going to try some introductory problems for Volume

Multiple Choice

What is the Volume of this shape: (Go Back to Slide 2 or 7 for Formulas or look them up in a separate tab)

• 2,201.5 m ³

• 1,995.7 m³

• 1,300. 7 m³

Multiple Choice

What is the volume of this shape?

• 125.5 in³

• 260.8 in³

• 290.8 in³

• 586.7 in³

Multiple Choice

What is the volume of this shape?

• 1436.76 in³

• 1523.8 in³

• 1602.45 in³

• 1804.7 in³

Now try some basic surface area problems: remember go back to slide 2 or slide 10 for formulas.

Multiple Choice

What is the surface area of this shape? (Right Rectangular Prism= 2(lh)+2(hw)+2(lh)

• 600 cm³

• 624 cm³

• 648 cm³

• 728 cm³

Multiple Choice

What is the surface area of this shape? (Right Square Pyramid: s²+ 2sl

(s=side l=slant height)

• 1503 m³

• 2021.6 m³

• 3023 m³

• 4242 m³

Rearranging Equations

• The last few questions will focus on just rearranging equations.

• You will always be told what variable to isolate and you just have to move variable by completing opposite operations

• You will use this when you are given the Area or Volume and asked to find a specific measurement for a shape.

On this problem, we isolated for H, by multiplying by 3 to remove the 1/3 to start.

We then had to divide by (pi)r² to undo the multiplication on the right.

Multiple Choice

Manipulate/Rearrange the following formulas:

• I/pr=t

• prI=t

Multiple Choice

Manipulate/Rearrange the following formulas:

• Ax-C=By

• y=Ax-C/B

• y=Ax+C/B

Multiple Choice

Manipulate/Rearrange the following equation to get V by itself:

• V=MP

• V=M/P

• V=P/M