Question

Estimate the number of pennies that would fit in a box one foot across by one foot wide by one foot tall. penny has a diameter of 0.75 inches and a thickness of about 0.06 inches.

Answer 1

The volume of the box is given by:

 $V1 = w * l * h$

Where,

w: width of the box

h: height of the box

l: length of the box

Substituting values:

$V1 = 1 * 1 * 1$

$V1 = 1 ft ^ 3$

The volume of the box in inches is:

 $V1 = 1 * (12 ^ 3)$

$V1 = 1728 in ^ 3$

Then, the volume of each penny is:

 $V2 = \pi * r ^ 2 * h$

Where,

r: coin radius

h: coin height

Substituting values:

 $V2 = 3.14 * (0.375) ^ 2 * (0.06)$

$V2 = 0.026 in ^ 3$

Then, the number of coins that fit in the box is:

 $N = \frac{V1}{V2}$

$N =\frac{1728}{0.026}$

$N = 66461$

Answer:

the number of pennies that would fit in the box is:

$N = 66461$