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### Course: Digital SAT Math > Unit 13

Lesson 1: Area and volume: advanced# Area and volume | Lesson

A guide to area and volume on the digital SAT

## What are area and volume problems?

Area and volume problems focus on using the relevant formulas for various two- and three-dimensional shapes. We'll be expected to calculate the length, area, surface area, and volume of shapes, as well as describe how changes in side length affect area and volume.

In this lesson, we'll learn to:

- Calculate the volumes and dimensions of three-dimensional solids
- Determine how dimension changes affect area and volume

**You can learn anything. Let's do this!**

## How do I calculate the volumes and dimensions of shapes?

### Volume word problem: gold ring

### Volume of a cone

### The volumes of three-dimensional solids

**Good news:**You

*do not*need to remember any volume formulas for the SAT! At the beginning of each SAT math section, the following volume formulas are provided as reference.

Shape | Formula |
---|---|

Right rectangular prism | |

Right circular cylinder | |

Sphere | |

Right circular cone | |

Rectangular pyramid |

If the test asks for the volume of a different shape, the volume formula will be provided alongside the question.

To calculate the volume of a solid:

- Find the volume formula for the solid.
- Plug the dimensions into the formula.
- Evaluate the volume.

**Example:**Fei Fei has a model of the Moon in the shape of a sphere. If the model has a radius of

Some questions will provide the volume of the solid and ask us to find a linear dimension such as length or radius.

To find an unknown dimension when the volume of a solid is given:

- Find the volume formula for the solid.
- Plug the volume and any known dimensions into the formula.
- Isolate the unknown dimension.

**Example:**A puzzle box is shaped like a rectangular prism and has a volume of

### Try it!

## How do changing dimensions affect area and volume?

### How volume changes when dimensions change

### Impact of increasing the radius

### The effect of changing dimensions on area and volume

When a linear dimension to the first power, e.g., the length of a rectangle or the height of a cylinder, changes by a factor, the area or volume changes by the same factor.

However, when a linear dimension to the second power, e.g., the side length of a square or the radius of a cylinder or cone, changes by a factor, the area or volume changes by

*the square of the factor*.### Try it!

## Your turn!

## Want to join the conversation?

- Calculating areas and volumes are so much easier when they give you the formula. Schools in my country make students remember the formula(88 votes)
- In my country you have to learn it except during national exams where they give it to you.(15 votes)

- if there was sat art, sal would get 800(40 votes)
- What is the best way to remember the formulas to each shape?(4 votes)
- The best thing is you don't have to remember! All the formulas will be given in the SAT question paper.(71 votes)

- Perfect I have the formulas, no need to think!!(33 votes)
- who is preparing for december SAT? any tips for english section? Is Erica Meltzer's Guide worth reading?(6 votes)
- I'm taking it in October (1 week) and fr I've 0 tips. I will pray whoever up there to get over 1490(14 votes)

- can someone explain the last question pls(9 votes)
- the circle with radius=x looks like dead pacman.(7 votes)
- The last question should be more explained.(7 votes)
- The change in radius is 2 (square that to get 4) and the change in height is 4. 4*2 = 8 so multiply the original volume by 8.(1 vote)

- im so confused about the last question, no variables were given in the question, where did 2 and 4 come from(2 votes)
- Formula of cone is 1/3πr^2h right so vol is 225 given in the question

Now when radius is twice the actual radius and height is also twice the actual height then we get

1/3*π(2r)^2*2h

1/3*π4r^2*2h

i.e. 8(1/3*πr^rh)

So 8 (225)= 1800(8 votes)

- I see that this lesson is easiest.(5 votes)