First Quiz
Calculate the area of the Big Island
of Hawaii as a percentage of the total area of Hawaii
Use the geothermal gradient to calculate
the temperature in the crust at a depth of 16 km
Second Quiz
Calculate the spreading rate for a Hawaiian
Islands as it drifts away from the Hawaiian Hot Spot
Calculate the subsidence (sinking) rate
of a Hawaiian volcano
Third Quiz
Convert the rate of flow of a pyroclastic flow from mi/hr to ft/s
Fourth Quiz
Calculate the rate of growth in m/1000
yr for a shield volcano
Calculate the volume of a Hawaiian shield
volcano
Fifth Quiz
Determine the absolute age of a rock sample
Calculate the area of the Big Island of Hawaii as a percentage of the total area of Hawaii
To calculate the percentage, divide the area of the Big Island of Hawaii by the total area of Hawaii (i.e. the entire state), and multiple the fraction by 100%.
The area of the Big Island is 10,451 km2.
The total area of Hawaii is 16,749 km2.
10,451 km2/16,749 km2 x 100% = 62.4%
To receive credit for the problem in class and on the quiz, you must show your work.
Use the geothermal gradient to calculate the temperature in the crust at a depth of 16 km
The geothermal gradient in the crust averages 30oC/km.
16 km x 30oC/km = 480oC
To receive credit for the problem in class and on the quiz, you must show your work.
Calculate the spreading rate for a Hawaiian Islands as it drifts away from the Hawaiian Hot Spot
To calculate the rate of drift for a Hawaiian Island, the distance of the island from the hot spot and the age of the island (time) is required. A rate is determined by the distance divided by the time: distance/time or, simply, d/t.
Rate = d/t
For example, the distance between Honolulu and Hilo is 300 km, and the age of O'ahu is approximately 2.5 million years. Calculate the average rate of drift for O'ahu.
d/t = 300km/2,500,000 yr = 0.00012 km/yr
To better visualize this rate, it should be converted to cm/yr. First convert kilometers to meters, then meters to centimeters.
300 km * 1000m/1 km = 300,000 m
300,000 m * 100 cm/1 m = 30,000,000 cm
Finally,
d/t = 30,000,000 cm/2,500,000 yr = 12 cm/yr
To receive credit for the problem in class and on the quiz, you must show your work.
Calculate the subsidence (sinking) rate of a Hawaiian volcano
To calculate the isostatic sinking rate of a Hawaiian volcano, divide the distance that the volcano sank by the age of the volcano. For example, if it took Mauna Loa 800,000 yr to sink 300 m:
d/t = 300 m/800,000 yr
To better visualize this rate, it should be converted to cm/1000 yr. First convert meters to centimeters:
300 m * 100cm/1 m = 30,000 cm
Finally, divide the distance in centimeters by the age of the volcano (time):
d/t = 300,000 cm/800,000 yr = 0.0375 cm/yr
To better visualize this rate, multiple the annual rate by 1000 to yield 1 cm/1000 yr
0.00375 cm/yr x 1000 = 37.5 cm/1000 yr
To receive credit for the problem in class and on the quiz, you must show your work.
Convert the rate of flow of a pyroclastic flow from mi/hr to ft/s
To convert mi/hr => ft/s, convert mi => ft and hr => s.
1 mi = 5280 ft
1 hr = 60 min
1 min = 60 s
Give a rate of 80 mi/hr:
80 mi/hr x 5280 ft/mi x hr/60 min x min/60 s = 117 ft/s
To receive credit for the problem in class and on the quiz, you must show your work.
Calculate the rate of growth in m/1000 yr for a shield volcano
To calculate the the growth rate for a shield volcano, you must know the total height and age of the volcano.
Mauna Loa is 9,000 m tall, from the sea floor, and at least 600,000 years old.
To calculate the rate in m/1000 yr, you can determine the rate in m/yr, then multiple by 1000.
Rate = 9000 m/600,000 yr = 0.015 m/yr
0.015 m/yr x 1000 = 15 m/1000 yr
To receive credit for the problem in class and on the quiz, you must show your work.
Calculate the volume of a Hawaiian shield volcano
Given the annual rate of lava production and the age of a shield volcano, you can calculate its volume.
If Mauna Loa erupts an average of 0.1 km3/yr and is at least 600,000 years old:
0.1 km3/yr x 600,000 yr = 60,000 km3
To receive credit for the problem in class and on the quiz, you must show your work.
Determine the absolute age of a rock sample
Use the concept of half-lives to determine the absolute of a rock sample.
A sample of granite has a U-235/Pb-207 ratio of 1/31. U-235 is the radioactive parent isotope, and Pb-207 is the daughter isotope.
The half-life of U-235 is 713 million years.
Determine the absolute age of this sample of granite:
P/D after one half-life = 50/50 or 1/1
P/D after two half-lives = 25/75 or 1/3
P/D after three half-lives = 12.5/87.5 or 1/7
P/D after four half-lives = 6.25/93.75 or 1/15
P/D after five half-lives = 3.125/96.875 or 1/31
Therefore, five half-lives have passed.
5 half-lives x 713 million years/half-life = 3.6 billion years
To receive credit for the problem in class and on the quiz, you must show your work.