Question

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?

Answer #1

A circular cone is 10 cm wide at the base and has a slant height
of 8.5 cm. Determine:
a. Volume of the cone =
b. Total surface area of the cone =
c. The angle the slant height makes with the base diameter =
d. The cylinder shown here has the same height and base radius
as the cone, by what percent the volume of
the cylinder exceeds the volume of the cone?

A cylinder is inscribed in a right circular cone of height 2.5
and radius (at the base) equal to 6.5. What are the dimensions of
such a cylinder which has maximum volume?
Asking for both radius and height.

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.

A paper cup in the shape of a cone with height 5 cm and radius 3
cm with the point of the cone at the bottom. A small leak develops
in the cup causing water to leak out at a rate of 0.1
cm3/s. Find the rate at which the height of the water in
the cup changes when the depth of the water is 2 cm. Recall that
the volume of a cone is v=1/3(pi)(r2)h

The
radius of a right circular cone is decreasing at a rate of
1.5cm/sec and the height is increasing at a rate of 5cm/sec. At
what rate is the volume changing when the height is 12cm and the
radius 2cm? Leave your answer in terms of pi.

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.

A tank in shape of an inverted right circular cone has height 10
m and radius 10 m. it is filled with 7 m of hot chocolate. Find the
work required to empty the tank by bumping the hot chocolate over
the top. density of chocolate equal 1510kg/m^3

A right circular cylinder is measured to have a mass of 1178.0
+/- 0.1 g, a diameter of 2.50 +/- 0.01 cm and a height of 30.48 +/-
0.01 cm.
a. Look up the volume equation for a right circular cylinder.
Remember that a radius is 1/2 the diameter.
b. The density is mass divided by volume. Find the density using
significant figures rules.
c. Find the density with error bars using the max/min
method.
d. Using a table of...

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*

10. A circular cylinder with a radius R of 1 cm and a
height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3
(r is a point on the z-axis, φ is an azimuthal angle). The cylinder
is then placed on the xy plane with its axis the same as the
z-axis. Find the electric field intensity E and the electric
potential V on point A on z-axis 2 cm from the top...

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