Question

In November 1987, a massive iceberg broke loose from the antartic ice mass and floated free in the ocean. The chunk of ice was estimated to be 98 mi long, 25 mi wide, and 750 ft thick. A typical backyard swimming pool contains about 24,000 gallons of water. How many of these pools could you fill from the water in this iceberg? (Assume the iceberg is a rectangular solid of the above dimensions and consists of water only). Express answer in scientific notation.

Answer 1

To calculate the number of backyard swimming pools that could be filled by the iceberg, the iceberg's dimensions are converted into feet and then calculated for volume in cubic feet. This volume is then converted to gallons, and divided by the volume of a typical pool. Finally, the result is expressed in scientific notation.

Step-by-step explanation:

To determine how many backyard swimming pools could be filled with the water from the iceberg, we first convert the iceberg's dimensions into a consistent unit of measure, calculate its volume, and then compare it with the volume of a typical pool.

We need to convert the dimensions of the iceberg from miles and feet into a unit consistent with the swimming pool's volume, which is in gallons. Since there are 5280 feet in a mile, and 1 cubic foot of water is approximately 7.48 gallons:

Length = 98 miles = 98 * 5280 feet

• Width = 25 miles = 25 * 5280 feet
• Thickness = 750 feet

Calculating the volume of the iceberg in cubic feet:

Volume of iceberg = (98 * 5280) * (25 * 5280) * 750 cubic feet

Now, converting the cubic feet into gallons by multiplying by 7.48:

Volume in gallons = Volume of iceberg * 7.48

To find the number of pools that can be filled:

Number of pools = Volume in gallons / 24,000 gallons per pool

We then express the number of pools in scientific notation as required.

Answer 2

`1.5964* 10^(10)` pools can be filled from the water in this iceberg.

Step-by-step explanation:

Length of an iceberg ,l= 98 miles =157.71 km

(1 mile = 1.60934 km)

Width of an iceberg,w = 25 miles = 40.23 km

Depth of an iceberg ,h= 750 feet = 0.2286 km

1 foot = 0.0003048 km

Volume of an iceberg, V= l × w × h =
`1,450.3923 km^3`

`1 km^3=10^(12) dm^3`

`V=1.4504* 10^(15) dm^3=1.4504* 10^(15) L`

`1 dm^3= 1L`

Number of swimming pools that can be filled by the water in an iceberg be x.

Volume of swimming pool = v = 24,000 gallons = 90,849.84 L

( 1 gal = 3.78541 L)

v =
`24,000 * 3.78541 L=90,849.84 L`

`x* v=V`

`x=(V)/(v)=(1.4504* 10^(15) L)/(90,849.84 L)`

`x=1.5964* 10^(10)`

`1.5964* 10^(10)` pools can be filled from the water in this iceberg.