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### Course: High school geometry>Unit 9

Lesson 4: Density

# Solid geometry FAQ

## Why do we need to know the difference between 2D and 3D objects?

Understanding the difference between 2D and 3D objects is important for solid geometry. 2D shapes, like squares and circles, only have length and width. 3D shapes, like cubes and spheres, also have depth. In order to find the volume and surface area of 3D shapes, we need to be able to identify them.

## What is Cavalieri's principle?

Cavalieri's principle states that two solids with the same height and cross-sectional area at every height have the same volume. This principle is useful for determining the volume of more complex shapes by breaking them down into simpler shapes that we already know how to find the volume of.

## How do we find the volume of a prism?

To find the volume of a prism, we use the formula $V=Bh$, where:
• $V$ is the volume
• $B$ is the area of the base of the prism
• $h$ is the height of the prism

## How do we find the volume of a pyramid?

To find the volume of a pyramid, we use the formula $V=\frac{1}{3}Bh$, where:
• $V$ is the volume
• $B$ is the area of the base of the pyramid
• $h$ is the height of the pyramid

## How do we find the surface area of a prism or pyramid?

To find the surface area of a prism (or a pyramid), we add up the areas of all of its faces.

## What is density and why is it important?

Density is a measure of how compact a material is. It is defined as the mass of the material divided by its volume. In solid geometry, we can use density to compare different materials and determine which one is heavier or lighter for a given volume.

## How are these topics used in the real world?

There are countless applications of solid geometry in the real world! For example, architects and engineers use concepts like volume and surface area to design buildings, bridges, and other structures. In manufacturing, density is an important consideration when selecting materials. And in science, researchers often use dissection methods to study the internal structure of an object.

## Want to join the conversation?

• I'm confused: Is Cavalieri's principle related to density? And if so, how?
• What alex81 said. (in comments)

Cavalieri's principle has no mention of density and only works with Volume, Area, and Lengths of the 3D shapes. No Quantities.
• wait, I'm confused, what is the difference between area and volume density and how do i know which formula to use?
• Area is simply volume in 2D. To figure out the density for a 3D object, let's say a Rectangular-Based Pyramid, we need to find the volume first.

The formula is 1/3*(l*w)*h. The (l*w) is the area of the base of the Pyramid. To find the volume you would multiply the base area by the height, and then by 1/3. Furthermore, to find the density you would need the quantity and the volume you just solved for to find the density in this equation:

Quantity / Volume = Density

To answer your question, you can tell which formula to use by whether it's 3D or 2D. Density is just the next step after finding the area. (You can also find the density in a 2D object: Quantity / Area = Density)

Hope this helps!