Semester 2 Unit 5 –
5- 6
WKST
Name:
Mass and Density. A Graphing Calculator is allowed for these problems.
1.
A 10’ x 8’ rectangular sheet of a certain material has varying density. At any given distance of x feet from
1
the 8’ side of the sheet, the density can be estimated as
kg / ft². Find the mass of the sheet.
1  x3
2.
A rectangular bin contains sawdust such that the density varies with respect to its height. The density is
approximated by 42-2h kg / ft³. Find the mass if the bin has a base of 4 ft by 6 ft and a height of 3 ft.
3.
A circular oil spill has a density at r meters from its center given by
4.
60
a)
1 r2
If the oil spill extends to 2000 meters in radius, then find its mass.
b)
Within what distance is half the oil slick contained?
kg / m².
A rectangular shaped city lays along side a straight river. Its population decreases as you move away from
the river. The population can be estimated as 20 - 3x thousand per square mile.
a)
If the city is 10 miles in length along the river and 6 miles wide, then find its population.
b)
Suppose the city is semicircular in shape with a diameter of 10 miles. Find its population if
i)
the density varies as you move away from the center point along the river.
ii)
5.
If the temperature is constant, the density of the atmosphere as a function of height, h, is given by the
equation, p(h)  1.28e .000124h kg / m 3 .
a)
Find the mass of a pocket of air in the shape of a right circular cylinder with a radius of 10 meters and
10 meters high.
b)
6.
the density varies as you move away from the river.
Find the mass of the atmosphere 50 meters above sea level that surrounds the entire earth.
( note: the radius of earth is approximately 6730 km.)
Find the mass of the cone whose base radius is 9 ft, height is 18 ft, and whose density is given by the
equation, d (h)  10e .3 h kg / m 3 .
Answers:
1.
9.634 kg
3a.
2865.473 kg
4a.
2.
2808 kg
3b.
44.710 m
4bi. 392,699
4bii. 535,398
660,000
5a. 4018.746 kg
5b. 3.631 x 1016 kg
6. 5919.856 kg