Question

Image of one smaller cube labeled with fish food with dimensions of one-quarters feet on each side. Larger cube labeled shipping box with dimensions of length 3 and three fourths feet; width of 3 feet; height of 3 and one- quarter feet.Part 1: Understanding Volume 1. What is volume, and how is it measured?2. Look at the images above. How are the fish food box and the shipping box similar? How are they different?Part 2: Pack it up1. Just by looking at the images, what is your guess of how many fish food boxes can fit into the shipping box? How did you determine this? There is no right or wrong answer.2. Determine how many actual fish food boxes fit in the shipping box. Show your work.Part 3: The space inside1. Find the volume of the shipping box using the two methods and show your work:1. Packing cubes2. using the volume formula2. Explain how both methods provide the. same measurement of volume for the shipping box.

Answer 1

Given :

Fish food cube : dimensions of one-quarters feet on each side.

Shipping box : dimensions of length 3 and three fourths feet; width of 3 feet; height of 3 and one- quarter feet.

So, the volume = Length * width * height

The volume is measures in cubic feet

The volume of fish food cube =

`(1)/(4)\cdot(1)/(4)\cdot(1)/(4)=(1)/(64)ft^3`

The volume of shipping box =

`3(3)/(4)\cdot3\cdot3(1)/(4)=(585)/(16)=36(9)/(16)ft^3`

2. Look at the images above. How are the fish food box and the shipping box similar? How are they different?

Because both of them is a rectangular prism, both of them has length, width and height.

Part 2: Pack it up



1. Just by looking at the images, what is your guess of how many fish food boxes can fit into the shipping box? How did you determine this?

By dividing the volume of the shipping box by the volume of fish food

2. Determine how many actual fish food boxes fit in the shipping box. Show your work.

The number of fish food boxes =

`(585)/(16)/(1)/(64)=(585)/(16)*(64)/(1)=585*4=2340`

1. Find the volume of the shipping box using the two methods and show your work:

Using volume formula :

`V=l\cdot w\cdot h=3(3)/(4)\cdot3\cdot3(1)/(4)=(585)/(16)`

Using packing cubes :

by the number of cubes that can fit into the shipping box

There are 2340 cube and the volume of one cube is 1/64

So, the volume will be :

`2340\cdot(1)/(64)=(585)/(16)ft^3`

Explain how both methods provide the. same measurement of volume for the shipping box.​

Because both of them will give the same dimensions