The state of texas covers approxmiately 268,581 squared mi. During a hail storm the entire state is covered in 1billion meters of hail.(average radius of 1.4292cm)assume the hail falls so that the gaps of air are limited to 26% of the volume. As the state begins to warm, the hail melts.(piece of ice =.92g/mL)Determine the number of hail stones required
"1billion meters of hail"
Do you mean 1 billion m³ of hail?
We can calculate how many hailstones there were before they melted. What does melting (and the density of ice has to do with the problem?
Please recheck the exact wording of the question.
To determine the number of hail stones required, we need to calculate the volume of hail in the state of Texas and then divide it by the volume of a single hail stone.
1. Calculate the volume of the state of Texas:
The area of Texas is given as approximately 268,581 square miles, which is equivalent to 6.955 x 10^17 square centimeters (since 1 mile = 1609.34 meters and 1 meter = 100 centimeters).
The thickness of the hail covering the state is given as 1 billion meters, which is equivalent to 1 x 10^11 centimeters.
The volume of the state covered in hail is calculated by multiplying the area by the thickness:
Volume of Texas = Area x Thickness = 6.955 x 10^17 cm^2 x 1 x 10^11 cm = 6.955 x 10^28 cm^3
2. Calculate the volume of a single hail stone:
The average radius of a hail stone is given as 1.4292 cm, which means the diameter is twice the radius.
So, the diameter of a hail stone is 2 x 1.4292 cm = 2.8584 cm.
The volume of a hail stone is calculated using the formula for the volume of a sphere:
Volume of a hail stone = (4/3) x π x r^3, where r is the radius (1.4292 cm).
Volume of a hail stone = (4/3) x 3.1416 x (1.4292 cm)^3 ≈ 12.1405 cm^3
3. Calculate the number of hail stones required:
To determine the number of hail stones required, we divide the volume of Texas by the volume of a single hail stone:
Number of hail stones = Volume of Texas / Volume of a hail stone
Number of hail stones ≈ (6.955 x 10^28 cm^3) / (12.1405 cm^3)
Number of hail stones ≈ 5.7254 x 10^27 hail stones
Therefore, approximately 5.7254 x 10^27 hail stones are required to cover the state of Texas with a thickness of 1 billion meters during the hail storm.