Question

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?

Answer #1

Determine the total surface area of a cone that has a circular
base of radius 3 cm if the lateral portion of the cone (the side
that does not include the base) is made from a half-circle. Explain
your reasoning.

Find the dimensions of the right circular cone of maximum volume
having a slant height of a=20 ft.
(Use symbolic notation and fractions where needed.)
radius = ? ft
height = ? ft

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 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?

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...

determine which of these cylinders has the largest surface area
and show work
a. a cylinder with a height of 8cm and a base with a radius of
3cm
b. a cylinder with a height of 4 cm and a base with a radius of
8cm
c. a cylinder with a height of 8cm and a base with a radius of
4cm
d. a cylinder with a height of 6cm and a base with a radius of
3cm

A grain silo has the shape of a right circular cylinder
surmounted by a hemisphere. If the silo is to have a volume of
516π ft3, determine the radius and height of
the silo that requires the least amount of material to build.
Hint: The volume of the silo is
πr2h
+
A grain silo has
the shape of a right circular cylinder surmounted by a hemisphere.
If the silo is to have a volume of 516π ft3,
determine the...

A tank, shaped like a cone has height 99 meter and base radius
11 meter. It is placed so that the circular part is upward. It is
full of water, and we have to pump it all out by a pipe that is
always leveled at the surface of the water. Assume that a cubic
meter of water weighs 10000N, i.e. the density of water is
10000Nm^3. How much work does it require to pump all water out of
the...

A wooden cylinder has the dimension: diameter, d = 40 cm and
height, hcyl = 40 cm. The specific gravity of the wooden cylinder
is 0.6. A copper disc, with a diameter of 40 cm and height, hcu = 1
cm, is rigidly attached to the bottom end of the wooden cylinder.
The specific gravity of the copper disc is 8.8. The combination of
the wooden cylinder and copper disc is placed in the water with
their axis are in...

A grain silo has the shape of a right circular cylinder
surmounted by a hemisphere. If the silo is to have a volume of 498π
ft3, determine the radius and height of the silo that requires the
least amount of material to build. Hint: The volume of the silo is
πr^2h + 2 3 πr^3, and the surface area (including the floor) is
π(3r^2 + 2rh). (Round your answers to one decimal place.)
r= ft
h= ft

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