Question

the greatest volcanic eruption in recorded history took place in 1815 on the indonesian island of sumbawa, when the volcano tambora expelled and estimated 100 cubic kilometers of molten rock. suppose all of the ejected material fell on a region with an area of 600 square kilometers. find the average depth of the resulting layers of ash and rock.

Answer 1

`166(2)/(3)\ m`

Explanation:

Let

x ----> the average depth of the resulting layers of ash and rock

we know that

To find out the average depth, divide the cubic kilometers of molten rock by the area where all the ejected material fell.

so

`(100\ km^3)/(600\ km^2)=(1)/(6)\ km`

Convert to meters

Remember that

`1\ km=1,000\ m`

so

`(1)/(6)\ km=(1)/(6)(1,000)=(1,000)/(6)=(500)/(3)\ m`

Convert to mixed number

`(500)/(3)\ m=(498)/(3)+(2)/(3)=166(2)/(3)\ m`