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 = (V1)/(V2)`

`N =(1728)/(0.026)`

`N = 66461`

Answer:

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

`N = 66461`