Question

In: Math

Geometric Nets Suppose you could split open and flatten an ice cream cone. Before doing so,...

Geometric Nets

Suppose you could split open and flatten an ice cream cone.

Before doing so, you measure the circumference around the top of the cone and find it is 9.4 inches.

What is the radius of the opening of the cone approximated to the nearest tenth of an inch?Explain your answer.

Draw a picture of the flattened cone.

Explain how the circumference of the cone translates to the shape of your drawing.

Expert Solution

First consider the figure of a Cone as shown below:

The measure of the top red colored contour of the cone is the circumference of the cone.

The radius of the top opening which is actually a circle is denoted as .

We have to find the radius of opeing of the cone ( which is basically a circle ) when its circumference is given:

The formula for circumference is given by:

As given circumference =9.4 inches , Therefore:

When approximated to nearest tength, it becomes:

---------------------------------------------------------------------------------------------

When we cut open and flatten an ice cream cone, it's shape becomes as a sector of a circle having arc length of or equal to the circumference of the circle.

The picture of flattened cone is as follow:

---------------------------------------------------------------------------------------------------------

After opening of the cone, the circumference of the cone translates to the arc of a circle as shown in the picture above. The length of this arc is equal to circumference of the top circle of the cone (before opening).

milcah answered 2 years ago

Suppose an ice cream cone has negligible thickness and the tip of the cone is identified...

Suppose an ice cream cone has negligible thickness and the tip of the cone is identified with origin (0,0,0)and the circular opening at the top is identified with the equation x^2+y^2=1, z=1. if you fill the cone with ice cream "rounded" so that the surface of the sections forms part of the surface x^2+y^2+z^2=2 and the ice cream has variable density f= x^2+y^2+z^2, what is the mass of the ice cream?

. Suppose each ice cream truck has a marginal cost of $1.50 per ice cream cone...

. Suppose each ice cream truck has a marginal cost of $1.50 per ice cream cone sold and no fixed cost. Suppose the maximum number of ice cream cones sold by any one truck in a day is 100. If the price of an ice cream cone is $2, how many ice cream cones does each truck want to sell? If the industry is perfectly competitive will the price remain at $2 for an ice cream cone? If not, what...

Kilo-cone is an ice-cream store that sells 1kg ice cream cones, and has the following information:...

Kilo-cone is an ice-cream store that sells 1kg ice cream cones, and has the following information: Estimated monthly Sales (in cones) January to March: 45,000 per month April to September: 70,000 per month October to December: 20,000 per month Ice cream cones sell for $1 each from January 1st to March 31st, and $3 each during the rest of the year. Half of the sales are paid in cash, and the other half is on account. 90% of the sales...

The daily demand for ice cream cones at a price of $1.20 per cone is 50...

The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 cones. Use linear interpolation to estimate the demand at a price of $1.50 per cone.

Imagine that you have decided to open a small ice cream stand on campus called "Ice-Campusades."...

Imagine that you have decided to open a small ice cream stand on campus called "Ice-Campusades." You are very excited because you love ice cream (delicious!) and this is a fun way for you to apply your business and economics skills! Here is the first month's scenario--you order the same number (and the same variety) of ice creams each day from the ice cream suppliers, and your ice creams are always marked at $1.50 each. However, you notice that there...

Before purchasing the new ice cream truck, Cowboy Ice Cream, Inc. (CIC) considered eliminating the Retail...

Before purchasing the new ice cream truck, Cowboy Ice Cream, Inc. (CIC) considered eliminating the Retail Division. This was mainly prompted by Frank’s (W.T. fellow shareholder) concern that the income statements for the divisions for May-September 2017 (when the Retail Division is at full operation) imply that profitability could be improved if the Retail Division were eliminated. Division Retail Wholesale Sales $60,000 $160,000 Cost of goods sold (18,000) (90,000) Variable operating expenses required to operate each division (31,500) (15,050) Contribution...

2. Suppose a large size chocolate fudge ice cream gives 162 Calories. If an ice cream...

2. Suppose a large size chocolate fudge ice cream gives 162 Calories. If an ice cream contains 6.00 g of carbohydrate and 12.0 g of protein then find out grams of fat? [1g Fat = 9kcal, 1g Protein = 4kcal, and 1g Carbohydrate = 4kcal]

a frozen ice cream is placed into a container before the freezing process is complete. The...

a frozen ice cream is placed into a container before the freezing process is complete. The container has dimensions of infinite shapes 8, 10 and 12 cm and is then placed in a water blast freezer with a heat conductivity coefficient of 50W / (m2 K). product temperature of -14 degrees centigrade and air temperature of -25 degrees centigrade. product density is 700 Kg / m3, thermal conductivity (frozen) 1.2 W / (m K) and specific heat 1.9 kJ /...

4. a frozen cream ice is placed into the container before the freezing process is complete....

4. a frozen cream ice is placed into the container before the freezing process is complete. The container has a slinder-shaped dimension with a diameter of 3.5m and is then placed in a water blast freezer with a heat conductivity coefficient of -25 W (m2 k). product temperature of -11 c and air temperature of -25 c. product density is 700kg / m3. thermal conductivity (frozen) 1.2 W / (m K), and specific heat 1.9 kj (kg / K). if...

Suppose you are analysing the market for two goods - ice-cream and coffee. (i)Illustrate and explain...

Suppose you are analysing the market for two goods - ice-cream and coffee. (i)Illustrate and explain the impact each of the following would have on demand or supply of ice-cream. Also show how equilibrium price and quantity have changed. a. Cyclone Fani destroys part of the sugarcane crop and drives up the price of sugar b. Consumer income falls because of a recession and ice cream is considered a normal good. c. Producers expect the price of ice cream to...