Question

The dimeter of the base and the height of a cylindrical can are measured, and the measurement are known to have errors of at most 0.5cm. if the dimeter and height are taken to be 4cm and 6cm, respectively, estimate the maximum possible error in

a- the volume V of the cylindrical.

b- the surface area S of the cylindrical.

Answer #1

The radius and the height of a circular cone was measured and
found to be 10 cm and 30 cm with possible errors in measurement of
at most 0.1 cm and 0.05 cm respectively. What is the largest
possible error in using these values to compute the volume of the
cone?

A cylindrical can is to have volume 1500 cubic centimeters.
Determine the radius and the height which will minimize the amount
of material to be used.
Note that the surface area of a closed cylinder is
S=2πrh+2πr2 and the volume of a cylindrical can is
V=πr2h
radius =. cm
height = cm

The length, width, and height of a box are measured as 5 ft,
3 ft, and 7 ft, respectively, with an error in measurement of at
most 0.1 ft in each. Use differentials to estimate the maximum
error (in feet) in the calculated volume of the box.

The length, width, and height of a box are measured as 6 ft,
5 ft, and 3 ft, respectively, with an error in measurement of at
most 2/10 ft in each. Use differentials to estimate the maximum
error (in feet) in the calculated volume of the box.
*fraction form (exact asnwer) please, no decimals*

A model for the surface area of a human body is given by
S =
0.1096w0.425h0.725,
where w is the weight (in pounds), h is the
height (in inches), and S is measured in square feet. If
the errors in measurement of w and h are at most
6%, use differentials to estimate the maximum percentage error in
the calculated surface area. (Round your answer to one decimal
place.)

A cylindrical oil drum is to be designed so that its height plus
the diameter of its base is five feet. What is the maximum possible
volume for such a drum? [V = pi r^2 h]

240 square cm of metal is available to make a cylindrical can,
closed on the top and bottom. The can-making process is so
efficient that it can use all of the metal. What are the radius and
height of the can with the largest possible volume? Give exact
answers and approximate answers.
Volume of a cylinder: V = πr2h
Surface area of a cylinder: 2πr2 + 2πrh

A model for the surface area of a human body is given by S =
0.1091w^0.425 h^0.725, where w is the weight (in pounds) and h is
the height (in inches), and S is measured in square feet. If the
errors in measurements of w and h are at most 2%, use differentials
to estimate the maximum error in the calculated area.

The circumference of a sphere was measured to be 84 cm with a
possible error of 0.5 cm.
(a) Use differentials to estimate the maximum error in the
calculated surface area. (Round your answer to the nearest
integer.)
cm2
What is the relative error? (Round your answer to three decimal
places.)
(b) Use differentials to estimate the maximum error in the
calculated volume. (Round your answer to the nearest
integer.)
cm3
What is the relative error? (Round your answer to...

A manufacturer sends you 100m2 of material to construct a box
(single layer, closed top). The box must have a square base and be
of maximum volume. Let sbe side length the base of the box, and
hthe height of the box. a) Write an equation for the surface area
covered by the material. b) Determine a formula for the volume V as
a function of the side of s only. c) Determine the dimensions such
that of the box...

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