Question

A box has length 6 feet, width 3 feet, and height 7 inches. Find the volume of the box in cubic feet and in cubic inches. _____cubic inches _____cubic feet

Answer 1

The volume of the box is 10.5 cubic feet and 2592 cubic inches.

Step-by-step explanation:

The volume of a box can be found by multiplying its length, width, and height. In this case, the length is 6 feet, the width is 3 feet, and the height is 7 inches. To find the volume in cubic feet, we first need to convert the height to feet. Since there are 12 inches in a foot, the height is 7 inches / 12 inches/foot = 7/12 feet. Now we can calculate the volume:

Volume = length x width x height

Volume = 6 feet x 3 feet x (7/12) feet

Volume = 126/12 cubic feet

Volume = 10.5 cubic feet

To find the volume in cubic inches, we can simply convert all the dimensions to inches:

Volume = 6 feet x 12 inches/foot x 3 feet x 12 inches/foot x 7 inches

Volume = 2592 cubic inches

Answer 2

We need to find the volume of the given box in cubic inches and in cubic feet.

In order to do so, we can use the conversion:

`1ft=12in`

Thus, we have:

`\begin{gathered} 6ft=6\cdot12in=72in \\ \\ 3ft=3\cdot12in=36in \\ \\ 7in=7\cdot(1ft)/(12)=(7)/(12)ft \end{gathered}`

Thus, using the same units for the dimensions of the box, its volume V is:

`V=72in\cdot36in\cdot7in=(72\cdot36\cdot7)in^3=18144in^3`

Also:

`V=6ft\cdot3ft\cdot(7)/(12)ft=(6\cdot3\cdot(7)/(12))ft^(3)=10.5ft^(3)`

Therefore, the volume can be written as:

`\begin{gathered} 18144\text{ cubic inches} \\ \\ 10.5\text{ cubic feet} \end{gathered}`