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

Answer:

1.58  × 10∧16 pools.

Explanation:

Given:

Length of ice berg= 98 miles = 1557716 meters

Width of iceberg = 25 miles = 40233.6 meters

Thickness of iceberg = 750 ft = 230 meters

Volume of water in a swimming pool = 24,000 gallons = 90850 liters

The volume of the ice berg:

Volume = Length . width . thickness

Volume = 1557716 . 40233.6 . 230 = 1,441, 468, 016, 5248 m3 =  1,441, 468, 016, 5248 × 10 ∧3 L.

1 pool contains liters of water:  90850 liters

1,441, 468, 016, 5248 × 10 ∧3 liters contains = 1/90850 . 1,441, 468, 016, 524.8 × 10 ∧3 .

= 1.100 .  1,441, 468, 016, 5248 × 10 ∧3 L.

= 1.58  × 10∧16 pools.

Hence 1.6 × 10∧16 pools will be filled with that chunk of ice.

Answer 2

Answer:

$1.5964\times 10^{10}$ pools can be filled from the water in this iceberg.

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  = $1,450.3923 km^3$

$1 km^3=10^{12} dm^3$

$V=1.4504\times 10^{15} dm^3=1.4504\times 10^{15} L$

$1 dm^3= 1L$

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 = $24,000 \times 3.78541 L=90,849.84 L$

$x\times v=V$

$x=\frac{V}{v}=\frac{1.4504\times 10^{15} L}{90,849.84 L}$

$x=1.5964\times 10^{10}$

$1.5964\times 10^{10}$ pools can be filled from the water in this iceberg.