Question

4 The packing crate below is 3 feet long and 21 feet wide. It is filled completely with 648 boxes that measure a foot on each side. 4 3 ft 21 ft Part A: What is the height, in feet, of the packing crate? Show your work.

Answer 1

Given

Lenght of crate= 3 ft

Width of crate = 2.25 ft

Total number of boxes= 648

and edge of each box is 0.25 ft

Required

We need to find the height of crate and volume of crate.

Explanation

Here volume of each box is

$0.25^3=0.015625\text{ cubic feet}$

Let height of crate be h

Then

$3\times2.25\times h=0.015625\times628=9.8125$

i.e.

$h=\frac{9.8125}{6.75}=1.45$

So height of crate is 1.45 ft

Now volume of crate is

$3\times2.25\times1.45=9.8125\text{ cubic feet}$

This volume is same as that of 648 boxes. So we can either find the volume of crate in this way or alternatively we can find the volume of 648 boxes.