# Solve Difficult Problem: Average Density of Rectangular Parallelopiped

• jrzygrl
In summary, a rectangular parallelepiped is floating horizontally in a hot tub with 3.17 cm above the water surface. The task is to find the average density of the student. The suggested approach is to use geometry and possibly the buoyancy force.

## Homework Statement

A solid student in the shape of a rectangular parallelopiped of dimensions 28.0 cm x 19.1 cm x 2.000 m floats horizontally in a calm hot tub filled with warm water; 3.17 cm of the parallelopiped (along the 19.1 cm side) is above the water surface. Find the average density of the student.

## Homework Equations

maybe density, volume of parallelopiped

## The Attempt at a Solution

I have no idea how to solve this problem. I tried using geometry to find certain things but it did not help. Any help is appreciated!

i have a feeling it has something to do with the buoyancy force. you know anything about that?

… eureka … !

jrzygrl said:
I tried using geometry to find certain things but it did not help.

Hi jrzygrl!

A rectangular parallelepiped (no "o") (also called a cuboid) is just an ordinary rectangular box!

Hint: have you tried thinking about this in the bath, like Archimedes, and then running down the street completely naked, shouting "Eureka!" ?

## 1. What is a rectangular parallelepiped?

A rectangular parallelepiped is a three-dimensional geometric shape that has six rectangular faces and twelve edges. It is also known as a rectangular prism.

## 2. What is the average density of a rectangular parallelepiped?

The average density of a rectangular parallelepiped is the mass per unit volume of the object. It is calculated by dividing the total mass of the parallelepiped by its volume.

## 3. How do you calculate the volume of a rectangular parallelepiped?

The volume of a rectangular parallelepiped can be calculated by multiplying the length, width, and height of the object. The formula for volume is V = l * w * h.

## 4. What is the formula for calculating the average density of a rectangular parallelepiped?

The formula for calculating the average density of a rectangular parallelepiped is density = mass / volume. This means that the mass of the object is divided by its volume to determine the average density.

## 5. Can the average density of a rectangular parallelepiped change?

Yes, the average density of a rectangular parallelepiped can change. It can change if the mass or volume of the object changes. Additionally, the density can change if the shape of the object is altered, such as by stretching or compressing it.