September 16, 2019

You may not have realized it, but Oregon has four of the 18 most active volcanoes in the United States.  What percent of the country’s most active volcanoes is not in Oregon?  Express your answer to the nearest whole percent.

If four of the 18 most active volcanoes in the United States are in Oregon, then 14 of the 18 are not. This is equivalent to 14÷18 = 78%, to the nearest whole percent.

In addition to the known volcanoes in Oregon, a bulge that is rising out of the ground is catching the eye of scientists. The land area that the bulge covers is quite significant.  It is estimated to cover 100 square miles.  If the land area were in the shape of a square with an area of 100 square miles, what would be the perimeter of that square, in miles?  If the land area were instead in the shape of a perfect circle with an area of 100 square miles, what would be the circumference of that circle, in miles?  Express this answer to the nearest whole mile.

For a square with an area of 100 square miles and a side measuring s miles, we know A = s2, so 100 = s2 and when we take the square root of both sides, we get s = 10 miles. This would be a square with a perimeter of 4 × 10 = 40 miles. If we instead have a circle with an area of 100 square miles and a radius of r miles, we know A = πr2, so 100 = πr2.  Dividing both sides by π and then taking the square root of both sides, we see that r = 5.64 miles. This makes the diameter 2 × 5.64 = 11.28 miles. The circumference would then be C = πd = π × 11.28 = 35 miles, to the nearest whole number. 

It is believed that the bulge that is forming is probably a result of a pool of magma collecting below the earth’s surface, and that the amount of magma is equal in size to a lake 1 mile across and 65 feet deep.  Though lake bottoms are not in the perfect shape of a cone, we’ll assume it is the shape of a cone for estimation purposes. What is the volume, in cubic feet, of a right cone with a diameter of 1 mile and a height of 65 feet? Express your answer to the nearest million cubic feet.

The formula for the volume of a cone is V = (1/3)Bh, where B is the area of the circular base and h is the height of the cone. For this problem, we’re told that the height is 65 feet. The circular base has a diameter of 1 mile, which is 5280 feet. The radius is then 5280 × 2 = 2640 feet. The area of the circular base is π × r2 = π × 26402 = 21,895,644.16 square feet. The total volume of a cone with these dimensions is then (1/3)(21,895,644.16)(65) = 474,000,000 cubic feet, to the nearest million cubic feet.

  Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.

Page 2 contains ONLY PROBLEMS.