Question

What is the radius (in inches) of the base of a cone that will have the smallest possible surface area for a volume of 12.7 oz.? Vcone = 1/3πr2h SAcone = πr(r2+h2)1/2 + πr2 1 oz = 1.80468751 in3 Check your formulas with these values: for r=2 in and h=4 in, V=16.755 in3 and SA=40.666 in2

Answer #1

The diagram shows a toy. The shape of the toy is a cone, with
radius 4 cm and height 9 cm, on top of a hemisphere with radius 4
cm. Calculate the volume of the toy. Give your answer correct to
the nearest cubic centimetre. [The volume, V, of a cone with radius
r and height h is V = 3 1 πr 2h.] [The volume, V, of a sphere with
radius r is V = 3 4 πr 3.]

please please answer all of them
1. The lateral area of a cone is 49
in2 with a slant height of 7 in. Then the radius is
_____ in. Round answers to the nearest tenth.
2. The surface area of a cone with a radius of 3.3 cm and slant
height of 5 cm is _____ cm 2. Round answers to the
nearest tenth.
3. The surface area of a cone is 18.6 in2 with a
radius of 1.2 in....

Cones come in a few varieties, and we will consider the right
circular cone. A cone with a circular base is a circular cone. A
circular cone whose axis is perpendicular to the base is a right
circular cone.
1.Create a new class called
.Include a Javadoc comment at the top of the class. The Javadoc
comment should contain:
i.The name of the class and a (very) short description
ii.An @author tag followed by your name
iii.An @version tag followed...

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

A cylinder shaped can needs to be constructed to hold 400 cubic
centimeters of soup. The material for the sides of the can costs
0.04 cents per square centimeter. The material for the top and
bottom of the can need to be thicker, and costs 0.05 cents per
square centimeter. Find the dimensions for the can that will
minimize production cost.
Helpful information:
h : height of can, r : radius of can
Volume of a cylinder: V=πr2^h
Area of...

1. Suppose that you are standing on the ground, under the flight
path of an airplane. The airplane is flying at an altitude of 10
km. Using a radar device, you are able to detect that the plane is
currently 26 km away from you, and that its distance to you is
currently shrinking at a rate of 840 kilometers per hour. What is
the current speed of the airplane?
Hint: use the Pythagorean theorem to express a relationship
between...

a recreational lake created by an artificial damn has
the shape of a truncated cone. if the depth of water in the lake
(h) is 0 the radius of the lake would be r_1= 300meters. the radius
of the lake at it's surface is given in terms of the lake's depth
via the following relation r_2 = 300 + h.
a) given that the volume of a truncated cone is given
by the formula pi/3 × h(r(2/1)+ r(2/2) + r...

1. A six-sided box has a square base and a surface area of 54
m^2. Let V denote the volume of the box, and let x denote the
length of one of the sides of the base. Find a formula for V in
terms of x.
2. What is the maximum possible volume of the box in Problem 1?
Note that 0< x≤3√3.

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

MATH125: Unit 1 Individual Project Answer Form
Mathematical Modeling and Problem Solving
ALL questions below regarding SENDING A PACKAGE and PAINTING A
BEDROOM must be answered. Show ALL step-by-step calculations, round
all of your final answers correctly, and include the units of
measurement. Submit this modified Answer Form in the Unit 1 IP
Submissions area.
All commonly used formulas for geometric objects are really
mathematical models of the characteristics of physical objects. For
example, a basketball, because it is a...

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