In: Advanced Math

why the cylindrical shape of a can is the optimal shape

Needs to be 2 pages.

A machine produces metal pieces that are cylindrical in shape. A
sample of these pieces is taken and the diameters are found to be
1.02, 0.95, 1.03, 1.07, 0.98, 0.98, 0.99, 1.01, and 1.06
centimeters. Compute the sample mean x, the sample standard
deviation s and the median of the sample. Determine the 95%
confidence interval for the mean. Assume an approximately normal
distribution for the diameter random variable. (Hint: Use the
t–distribution.)

A cylindrical wire is bent into the shape of the quarter circle
C given by ? = ? ???(?) , ? = ? ???(?) , ? = ?, for 0 ≤ ? ≤ ?/2.
The density function is ?(?, ?, ?) = ?? ? . Determine the mass and
center of mass of the wire.

The dimension of the soil sample of a cylindrical shape is
provided in Figure 1. In its natural moist state, the soil sample
has the total weight of 1350 g before the water content
determination. The specific gravity, Gs of the soil is given as
2.72. The values obtained for the determination of water content
are: The mass of moist soil sample + mass of empty can = 1.415 kg;
the mass of fully dry soil sample + mass of...

1.
Show that the optimal efficiency of a cylindrical friction pump
occurs when α=-1.0
2. Calculate the maximum possible efficiency of a friction
pump
Notice: η = Power Attained / Power Expended

A wood stove is used to heat a single room. The stove is
cylindrical in shape, with a diameter of 40.0 cm and a length of
50.0cm and operates at a temperature of 400oF.
(a) If the temperature of the room is 70.0oF,
determine the anount of radiant energy delivered to the room by the
stove each second if the emissivity is 0.920.
(b) If the room is a square withwalls that are 8.00ft. high and
25.0 ft wide, determine...

A machine is producing metal pieces that are cylindrical
in shape. A sample of 12 pieces is taken and the diameters are:
1.01, 0.97, 1.03, 1.04, 0.8, 0.78, 1.06, 0.95, 0.87,1.0,0.88 and
0.90 centimeters.
a. Find 98% confidence interval for the true average diameter of
metal pieces produced by the machine.
We would like to test whether the true average diameter
of metal pieces produced by the machine is less than 1
centimeter.
b. Assuming the population distribution is approximately...

1. A machine produces metal pieces that are cylindrical in
shape. A sample of 36 metal pieces is taken and the mean diameters
for this sample was 6.21 centimeters. In addition from previous
studies it is know that the population is approximately Normal with
a standard deviation 1.84centimeter.
Note: Do the calculations by hand, but show the R code and
output for the z-value, t-value or for finding area under the
standard normal curve.
Note: Round your numbers to exactly...

Consider cylindrical shape rod of silicon with circular
cross-section (resistivity of 3345 , the diameter of 2.53 cm and
length of 32.7 cm). Consider a voltage of 1.25*103 V is applied.
The temperature coefficient of silicon is -0.005 0C-1 (negative
because Silicon is a semiconductor).
(a) Find the resistance of this rod at room temperature? (2
points)
(b) Find the electric field inside the silicon rod? (3
points)
(c) Find the energy dissipations in 3 min? (2 points)
(d) If...

A plasma of uniform charge density po= is
contained within a cylindrical shape, of infinite length and radius
ro. With what speed must a particle of mass m and charge
q perpendicularly strike the cylinder in order to bring it to rest
at the center of the cylinder?

Sea cucumbers (see figure) are classic hydrostats- cylindrical
in shape with a body wall surrounding a constant volume of water.
Many sea cucumber species crawl along the substrate using
peristaltic locomotion (waves of alternating muscle contraction)
while some species burrow into the substrate, which requires force
to displace sediment. How might (a) the fiber angle of the
collagenous body wall and (b) the initial shape of the animal
correlate with peristaltic locomotion versus burrowing?

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