1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marina CMI [18]
3 years ago
13

A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5

y is 10.5 and r=3 If both containers have labels covering their lateral surfaces, which container will have less label area and by how much? Container Y by about 42 in.2. Container X by about 28 in.2. Container Y by about 9 in.2. Container X by about 85 in.2.

Mathematics
1 answer:
KatRina [158]3 years ago
5 0

Answer:

Container \rm X will have less label area than container \rm Y by about 9\; \rm in.

Step-by-step explanation:

A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.

Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of h and a radius of r at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width h and length 2\,\pi\, r.

Apply this reasoning to both cylinder \mathrm{X} and \rm Y:

For cylinder \mathrm{X}, h = 6\; \rm in while r = 4.5\; \rm in. Therefore, when the lateral side of this cylinder is unrolled:

  • The width of the rectangle will be 6\; \rm in, while
  • The length of the rectangle will be 2 \, \pi \times 4.5\; \rm in = 9\, \pi\; \rm in.

That corresponds to a lateral surface area of 54\, \pi\; \rm in^2.

For cylinder \rm Y, h = 10.5\; \rm in while r = 3\; \rm in. Similarly, when the lateral side of this cylinder is unrolled:

  • The width of the rectangle will be 10.5\; \rm in, while
  • The length of the rectangle will be 2\pi\times 3\; \rm in = 6\,\pi \; \rm in.

That corresponds to a lateral surface area of 63\,\pi \; \rm in^2.

Therefore, the lateral surface area of cylinder \rm X is smaller than that of cylinder \rm Y by 9\,\pi\; \rm in^2.

You might be interested in
Three boxes are stacked one on top of the other. One box is 5 feet 10 inches tall , one is 4 feet 2 inches tall and one is 2 fee
katovenus [111]
The boxes would be 12 feet and 3 inches tall
6 0
3 years ago
The slope of the line that passes through the point (17,20) and (1,-8) is
AlladinOne [14]

Answer:

y = m x + b      standard form of equation for straight line\

        m = (y2 - y1) / (x2 - x1) = (20 - -8) / 17 - 1) = 28 / 16

        m = 7 / 4

8 0
2 years ago
Help me plzzzzzzzzzzzzzzzz​
Yuliya22 [10]

Answer: 22.99

15 percent of (19.99 U.S. dollars) =

2.9985 U.S. dollars

Disclaimer - More info

Tip Calculator

Bill

19.99

Tip %

15%

Number of people

1

Tip

$3.00

Total

$22.99

7 0
3 years ago
Read 2 more answers
Look at the middle 9 of .999. What is the value of the 9 to it's right?
Zepler [3.9K]

Answer:

The value would be thousandths.

Step-by-step explanation:

3 0
2 years ago
Mr. Jennings is shopping for a car loan. He wants to buy a car that costs $18,000. He plans to pay $5,000 in cash and get a loan
Ugo [173]

Answer:

$650

Step-by-step explanation:

Interest = amount of the loan x interest rate x time

Amount of the loan = price of the car - cash payment

$18,000 - $5,000 = $13,000

interest rate = 5%

time = 1 year

$13,000 x 0.05 x 1 = $650

3 0
2 years ago
Other questions:
  • M is the midpoint of AB, M is (7,2) and A is (6,7), what is the coordinate of B
    8·1 answer
  • What us the average rate of change
    10·1 answer
  • Please solve <br> 5/5 ÷ 1/2 =
    8·1 answer
  • What value of s makes the equation true? 14s−4−23s=5
    6·1 answer
  • rob needs 345 centimeters of tape to wrap packages. how many rolls of tape should rob buy if each roll holds 1 meter of tape
    10·1 answer
  • Hey I am on the phone I don’t want you guys going out for a while
    15·2 answers
  • Which expression entered into a graphing calculator will return the probability
    9·1 answer
  • Help please. Due Friday
    7·1 answer
  • Multiply.
    10·1 answer
  • Genes are sections of DNA that code for a particular trait. Genes are?<br>​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!