Practice Page

Directions: Read carefully. Be sure to show your work.

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1.
As of 2015, the most densely populated state in the US was New Jersey. The 2015 population of New Jersey was 8,957,907 people with 1218.1 people per square mile. Which choice is the approximate land area of the state of New Jersey to the nearest square mile?
newjerseyAtlantic City, New Jersey
Choose:
 
7,135 square miles
7,354 square miles
 
10,912 square miles
12,354 square miles



2.
The average amount of pasture needed to feed mature mules is 1 acre per mule. A farm has three rectangular fenced pasture sections: 100 ft. by 300 ft., 150 ft. by 500 ft., and 250 ft. by 400 ft. to be used for grazing.
1 acre = 43,560 square feet.
mules
Six mules are being adopted from a rescue program. The farm does not have sufficient pasture space to support 6 mules according to the 1 acre per mule guideline. What is the least amount of additional square footage of grazing land that will need to be fenced to meet this guideline?



3.
Ninety-eight cut boulders are being brought in to help prevent further erosion on a portion of this coastline. Each boulder has been roughly cut into a cube with sides of length 0.8 meters. The stone in the boulders has an average density of 3000 kg/m3.
beach erosion
  a) Find the average weight (mass) of each boulder in pounds. (Round to the nearest ten pounds.)

b) A dump truck with a carrying capacity of 28,000 pounds is used to transport the boulders to the coastline. How many trips will the truck need to make to transport all of the boulders? Assume the truck does not exceed its carrying capacity.
 



4.
An air conditioner is being purchased for the room shown at the right. The room has an open ceiling that follows the roof trusses. According to the US Department of Energy, to determine the cooling requirement of a room, use 2.5 BTUs per cubic foot of air space. To this value, add an additional 1000 for each window in the room. This room has 4 windows.
Determine the number of BTUs needed to cool this room.



5.
Astronauts on the International Space Station may lose an average of 1% of their bone mineral density, BMD, per month due to the reduced gravity environment, as compared to an average loss of 1% per year on Earth.
ISS International Space Station (ISS)
Photo courtesy of NASA
  Astronauts returning to Earth may be at an increased risk of a fracture.
BMD is measured in milligrams per square centimeter of bone surface. (Assume that bone loss is constant for this problem and that no measures are taken to reduce the loss.)
a) An astronaut's preflight BMD is 1040.0 mg/cm2. At a loss of 1% per year, what would be the astronaut's BMD after one year on Earth?

b) At a loss of 1% per month, what would be this astronaut's BMD after two months?

c) At a loss of 1% per month, what would be this astronaut's BMD after one year on the ISS?

d) At a BMD loss of more than 20%, an individual becomes prone to fractures. After how many months on the ISS does this astronaut become prone to fractures?

FYI: Bone density loss can be reduced with supplements and resistance exercise.



6.
Bamboo is a very renewable source of material for flooring and other "wood" products. A bamboo plant can grow to a 13" diameter with a height of 100 feet in two years. In 5 years, it matures to its maximum strength, and if not harvested, it decays and rots. In harvesting, the plant is cut off near the base of the plant, and, unlike trees, a new plant emerges from the same root.
The wood floors created from bamboo can be stronger than oak floors.
bamboo
 
One plant can create enough processed bamboo stranded fiber to produce a floor board that measures 16" length, 4" width and ½" thickness. The processed bamboo has a density of 39 lbs/ft3 and is sold to floor manufacturers at the rate of $2.25 per pound.
If the Green Flooring Company has $20,000 to initially invest in the new bamboo flooring, how many bamboo plants must be harvested to fill the order?



7.
An older method of estimating body fat percentage was to measure a person's average density (total mass divided by total volume), and apply a formula to convert to a body fat percentage.
Formula: BF = (4.57/p - 4.142) x 100
where BF = body fat and p = density in g/cm3

A man weighs 175 pounds. His total body volume is modeled by a cylinder with a height of 170 cm and a radius of 12 cm.

Find his body fat percentage, based upon the given formula (to the nearest percent).
treadmill2
 



8.
A kitchen was remodeled and granite counter tops were installed. A rectangular island in the kitchen now has a granite top measuring 5 ft. by 8 ft. by 1.2 inches. The density of granite is 2.7 g/cm3.

How much does the granite top on the island weigh, in pounds?
(Round to nearest tenth of a pound.)



9.
In the movie, Raiders of the Lost Ark, archaeologist Indiana Jones replaces a solid Golden Idol with a bag of sand. The idol rested on a platform which precisely counterbalanced the temple's ancient self-destruct mechanism.
The idol can be modeled by a cylinder with a height of 18 cm and a radius of 6 cm. The density of gold is 19.32 g/cm3. The density of sand is 1.6 g/cm3.
raiders
 
a) What was the mass (weight) of the idol in pounds?

b) What was the needed volume of sand to avoid tripping the self-destruct mechanism (in cm3 )?



10.
During a renovation project, a section of fencing that separated a pool from a horse pasture was temporarily taken down. When the workmen weren't looking, horse "Lily", ventured into the pool area and fell into the pool. The fiberglass steps could not support her weight, so a ramp was built to walk her out of the pool.

waterlily
The black mat seen in the photo is not the "ramp". This mat was placed near the stairs to stabilize the horse's footing when the ramp was used for her escape.

 
The ramp was composed of 6 treated lumber boards measuring 2 in. by 6 in. by 8 ft., weighing 17 pounds each, and a series of smaller treated lumber cross boards. The ramp was substantially heavy!
When the ramp was lowered into the water, it floated!!!!
Establish mathematically "WHY" this heavy ramp floated.

Good news: After 5 hours of pondering, Lily did work up the courage to walk up the ramp (held down by two people standing on either side) to safety. Thankfully she was not injured, but the pool liner was destroyed by her horseshoes.

 


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