Question

a cylindrical can holds 250 ml of liquid. Find the dimensions of the can (radius and height) that will minimize the amount of material used (surface area). Please show your work. Thank you.

Answer #1

A manufacturer makes a cylindrical can with a volume of 500
cubic centimeters. What dimensions (radius and height) will
minimize the material needed to produce each can, that is, minimize
the surface area? Explain and show all steps business calculus.

A cylindrical can, open at the top, is to hold 220 cm3 of
liquid. Find the height and radius that minimize the amount of
material needed to manufacture the can. Enter your answer with
rational exponents, and use pi to represent ?.

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

A cylindrical can, open at the top, is to hold 830 cm3 of
liquid. Find the height and radius that minimize the amount of
material needed to manufacture the can. Enter your answer with
rational exponents, and use pi to represent π

A company needs to make a cylindrical can that can hold
precisely 0.7 liters of liquid. If the entire can is to be made out
of the same material, find the dimensions of the can that will
minimize the cost. Round your answer to the nearest two decimal
places.

A company wants to design an open top cylindrical bin with
volume of 250 cm3. What dimensions, which are the radius r and
height h, will minimize the total surface area of the bin? Round to
one decimal place. (hint: consider bin disassembled for area of the
side) Geometry formulas: Area of a circle is ? = ??2, Volume of a
cylinder is ? = ??2h, and circumference of a circle is ? = 2??. Use
? = 3.14

An open cylindrical trashcan is to hold 12 cubic feet of
material. What should be its dimensions if the cost of material
used is to be a minimum? [Surface Area, S = πr^2 + 2πrℎ where r =
radius and h = height.]

( PARTA) Find the dimensions (both base and height ) of the
rectangle of largest area that has its base on the x-axis and its
other two vertices above the x-axis and lying on the parabola
below. y = 8 − x
(PARTB) A box with a square base and open top must have a volume
of 62,500 cm3. Find the dimensions( sides of base and
the height) of the box that minimize the amount of material
used.

A cylindrical can is built to store a food. This can is
constructed without a lid and must contain 100cm3 of volume. Find
the radius and height of this cylinder so that the amount of
material used in its manufacture is minimal.

A grain silo consists of a cylindrical concrete tower surmounted
by a metal hemispherical dome. The metal in the dome costs 2.1
times as much as the concrete (per unit of surface area). If the
volume of the silo is 600m^3
what are the dimensions of the silo (radius and height of the
cylindrical tower) that minimize the cost of the materials?
Assume the silo has no floor and no flat ceiling under the
dome.
What is the function of...

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