Calculating areas and volumes are so much easier when they give you the formula. Schools in my country make students remember the formula

In my country you have to learn it except during national exams where they give it to you.

For me, trigonometry and geometry math has been the hardest math.

Trigonometry is one of my favorite parts in Math (after Calculus, of course). It's something that you'll get with constant practice. Just solve more questions, and you will begin to see a pattern forming.

who is preparing for december SAT? any tips for english section? Is Erica Meltzer's Guide worth reading?

I'm taking it in October (1 week) and fr I've 0 tips. I will pray whoever up there to get over 1490

What is the best way to remember the formulas to each shape?

The best thing is you don't have to remember! All the formulas will be given in the SAT question paper.

Main content

Course: Digital SAT Math > Unit 13

Lesson 1: Area and volume: advanced

Area and volume | Lesson

Google Classroom

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

Khan Academy video wrapper

Volume word problem: gold ringSee video transcript

Volume of a cone

Khan Academy video wrapper

Volume of a coneSee video transcript

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	$V = ℓ w h$ ‍
Right circular cylinder	$V = π r^{2} h$ ‍
Sphere	$V = \frac{4}{3} π r^{3}$ ‍
Right circular cone	$V = \frac{1}{3} π r^{2} h$ ‍
Rectangular pyramid	$V = \frac{1}{3} ℓ w h$ ‍

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

10

centimeters, what is the volume of the model in cubic centimeters?

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

240

cubic inches. If the puzzle box has a length of

10

inches and a width of

8

inches, what is the height of the puzzle box in inches?

Try it!

try: find the volume of a pyramid

A pyramid has a square base with a side length of

8

centimeters. The height of the pyramid is

\frac{3}{4}

as long as the side length of its base.

What is the height of the pyramid in centimeters?

What is the volume of the pyramid in cubic centimeters?

How do changing dimensions affect area and volume?

How volume changes when dimensions change

Khan Academy video wrapper

How volume changes from changing dimensionsSee video transcript

Impact of increasing the radius

Khan Academy video wrapper

Impact of increasing the radiusSee video transcript

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!

try: compare the volumes of two cylinders

Right circular cylinder

A

has a volume of

64 π

cubic feet. Which of the following right circular cylinders have the same volume as cylinder

A

(Choice A)
A cylinder with $2$ ‍ times the radius and $\frac{1}{2}$ ‍ the height of cylinder $A$ ‍
(Choice B)
A cylinder with $2$ ‍ times the radius and $\frac{1}{4}$ ‍ the height of cylinder $A$ ‍
(Choice C)
A cylinder with $\frac{1}{2}$ ‍ the radius and $8$ ‍ times the height of cylinder $A$ ‍
(Choice D)
A cylinder with $\frac{1}{3}$ ‍ the radius and $9$ ‍ times the height of cylinder $A$ ‍

Your turn!

practice: calculate a volume

What is the volume, in cubic meters, of a right rectangular prism that has a length of

2

meters, a width of

0.4

meter, and a height of

5

meters?

practice: calculate a linear dimension

A medicine bottle is in the shape of a right circular cylinder. If the volume of the bottle is

144 π

cubic centimeters, what is the diameter of the base of the bottle, in centimeters?

practice: determine the effect of scaling on volume

The volume of a right circular cone

A

225

cubic inches. What is the volume, in cubic inches, of a right circular cone with twice the radius and twice the height of cone

A

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Calculating areas and volumes are so much easier when they give you the formula. Schools in my country make students remember the formula
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who is preparing for december SAT? any tips for english section? Is Erica Meltzer's Guide worth reading?
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the circle with radius=x looks like dead pacman.
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can someone explain the last question pls
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The last question should be more explained.
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- StudyBuddy
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  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.
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