How many dimes fit into a 5 gallon water jug?

Answer 1

To estimate how many dimes fit into a 5-gallon water jug, we can start by calculating the volume of both the jug and a dime:

1. **Volume of a 5-gallon jug**:
   1 gallon = 231 cubic inches
   So, 5 gallons = 5 × 231 = 1,155 cubic inches

2. *Volume of a dime*:
   A dime has a diameter of about 0.705 inches and a thickness of about 0.053 inches.
   The volume ( V ) of a cylinder is given by the formula:
   [ V = \pi r^2 h ]
   where ( r ) is the radius and ( h ) is the height (thickness).

   • Radius of a dime = 0.705 inches / 2 = 0.3525 inches
   • Height (thickness) of a dime = 0.053 inches

   Volume of a dime:
   [ V = \pi (0.3525)^2 (0.053) \approx 0.0209 \text{ cubic inches} ]

3. *Estimating the number of dimes*:
   Divide the total volume of the jug by the volume of a dime:
   [ \frac{1,155 \text{ cubic inches}}{0.0209 \text{ cubic inches per dime}} \approx 55,263 \text{ dimes} ]

So, approximately 55,263 dimes can fit into a 5-gallon water jug, assuming efficient packing and no wasted space.

Answer 2

To estimate how many dimes fit into a 5-gallon water jug, you'll need to approximate the volume of the jug and the volume of a dime.

Volume of the Jug:

1 gallon is approximately 3.785 liters.

Therefore, 5 gallons is about 18.925 liters.

Volume of a Dime:

A U.S. dime has a diameter of about 17.91 mm and a thickness of 1.35 mm.

The volume of a cylindrical dime can be approximated using the formula for the volume of a cylinder:

𝑉

=

𝜋

𝑟

2

ℎ

V=πr

2

h.

Radius

𝑟

r is half of the diameter, so

𝑟

≈

8.955

r≈8.955 mm.

Height

ℎ

h is the thickness of the dime, 1.35 mm.

Converting to liters:

𝑉

≈

𝜋

×

(

0.008955

)

2

×

0.00135

≈

3.89

×

1

0

−

8

V≈π×(0.008955)

2

×0.00135≈3.89×10

−8

liters.

Calculate the Number of Dimes:

Volume of the jug in liters / Volume of a single dime in liters:

18.925

 liters

/

3.89

×

1

0

−

8

 liters

≈

4.86

×

1

0

9

 dimes

18.925 liters/3.89×10

−8

 liters≈4.86×10

9

 dimes.

However, this calculation assumes no gaps between the dimes, which isn't realistic due to the packing efficiency of spherical objects. In practice, the packing efficiency of dimes is around 60%, so you should adjust the number:

Adjusted number of dimes:

4.86

×

1

0

9

 dimes

×

0.60

≈

2.92

×

1

0

9

 dimes

4.86×10

9

 dimes×0.60≈2.92×10

9

 dimes.

Thus, approximately 2.92 billion dimes would fit into a 5-gallon water jug considering realistic packing efficiency.