Given: C = 10 cm, dC = 0.4 cm

Part (a) calculated values of the radius:

or solved for radius:

The slope of the radius as a function of the circumference.

Note: the slope is a constant (see Fig 1).

dr is the change in the linearization of r that results from a change in dC and is calculated thus:

Domain:

the predicted rise in r for an increase (dC = 0.4) is:

The estimated % change is:

The true % change in the radius as the circumference is changed from 10 to 10.4 cm is 4.0 as shown to the right:

NO error between estimated % change and true % change since the radius - circumference equation had a constant slope.

(percent error)

Part (b) calculated values of the surface area (from the radius):

at

for a C increase = 0.4

surface area formula:

(surface area at C = 10 cm)

first derivative:

(change in cm² of the surface area)

estimated change

(decimal increase in cm² from a C =10 to a C = 10.4.)

estimated percentage change:

(percent increase from C = 10 to C = 10.4))

The true % of change as the circumference is changed from 10 cm to 10.4 cm is:

(% error due to the linearization of the surface area equation with C increasing from 10 to 10.4 cm. The estimated area was approximately 1.961% too low... why? Would the error be more or less if C was say 20 cm?... why??)

Error:

Part (c) calculated values of the volume (calculated from the radius):

at

for a C increase = 0.4

volume formula:

(volume at C = 10 cm)

first derivative:

estimated change

(decimal increase in cm³ from a C =10 to a C = 10.4.)

estimated percentage change:

(percent increase from C = 10 to C = 10.4)

The true % of change as the circumference is changed from 10 cm to 10.4 cm is:

(% error due to the linearization of the volume equation. The estimated area was approximately 3.892% to low... why? Would the error become larger with increasing values of C?... why? Would the linearization surface area or linearization of volume produce the greater error?... why? )

Error:

radius

surface area

volume

Graphing Domain