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
Vera_Pavlovna [14]
3 years ago
10

An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diamet

er. The company wants to sell a larger can of juice. The height of the can is kept at 9.4 cm, but the diameter is increased to 8.5 cm. About how many times more juice will the new can hold?
Image is the same question w/ a model.

Mathematics
1 answer:
drek231 [11]3 years ago
3 0
<h2>Hello!</h2>

The answer is:

The third option:

2.7 times as much.

<h2>Why?</h2>

To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.

So, calculating we have:

Old can:

Since the cans have a right cylinder shape, we can calculate their volume using the following formula:

Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h

Where,

r=radius=\frac{diameter}{2}\\h=height

We are given the old can dimensions:

radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm

So, calculating the volume, we have:

Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}

We have that the volume of the old can is:

Volume_{Can}=199.7cm^{2}

New can:

We are given the new can dimensions, the diameter is increased but the height is the same, so:

radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm

Calculating we have:

Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}

Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:

\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7

Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:

2.7 times as much.

Have a nice day!

You might be interested in
Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(4​,5​), ​(-6​,-6​), and ​(-14​,2​
Lilit [14]

Answer:

  (-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

  (x -4)^2 +(y -5)^2 = 10^2

  x^2 -8x +16 +y^2 -10y +25 = 100

  x^2 +y^2 -8x -10y = 59

__

The epicenter is 5 units from Y, so lies on the circle ...

  (x +6)^2 +(y +6)^2 = 5^2

  x^2 +12x +36 +y^2 +12y +36 = 25

  x^2 +y^2 +12x +12y = -47

__

The epicenter is 13 units from Z, so lies on the circle ...

  (x +14)^2 +(y -2)^2 = 13^2

  x^2 +28x +196 +y^2 -4y +4 = 169

  x^2 +y^2 +28x -4y = -31

__

Subtracting the second equation from each of the other two, we get ...

  (x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

  -20x -22y = 106 . . . . eq1 -eq2

  (x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

  16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

  x = y+1 . . . . . from eq3 -eq2 divided by 16

  10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

  21y = -63 . . . . . . . . . . . . simplify, subtract 10

  y = -3

  x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

8 0
3 years ago
Find the product of each sum and difference. (2l + 9)(2l – 9)
Alex787 [66]

Answer:

360

Step-by-step explanation:

(i think that is a 1 not an L)

21 + 9 equals 30. And 21-9 equals 12. So you would multiply 30*12 which gives you your answer!

<h2>360</h2>
4 0
3 years ago
The following chart shows the times of runners in the 100 meter sprint.
scoray [572]

Answer:

Miguel

Step-by-step explanation:

Miguel had..

.04 less than Tyrone

.28 less than Rahn

.23 less than George

4 0
2 years ago
Read 2 more answers
The art teacher bought 1,500 beads for a new art project. 25% of the beads are red, 35% of the beads are green, the rest of the
Pavlova-9 [17]
40% or 600.

1500 x .4
5 0
3 years ago
Given the geometric sequence where a_1 = 3 and r = √2 find a_9
sesenic [268]
To find n-therm of a geometric sequence, we are going to use the formula a_{n} =a _{1} r^{n-1}
where:
a_{n} is the term we are looking for
a _{1} is the first term 
r is the ratio 
n is the position of the number in the sequence 

From the question we now that a _{1} =3, r= \sqrt{2}, and n=9. Lets replace those values into our formula to get:
a _{9} =3( \sqrt{2} )^{9-1}
a_{9} =3 \sqrt{2} ^{8}
a_{9} =48

We can conclude that in our geometric sequence a_{9} =48; therefore, the answer is A.
4 0
3 years ago
Other questions:
  • If f(x) = 4x - 3, evaluate f(2).
    7·1 answer
  • Enter the correct unit of measurement to complete the conversion. 100 liters = 1 what?
    11·1 answer
  • What is the area of the obtuse triangle below?
    5·1 answer
  • Do you guys know how to do this problem I’m stuck school just Started and I can’t remember how to do this
    10·1 answer
  • What’s the difference need help
    9·1 answer
  • Dan, David, Thor, and Charles together clean out evil from 60 cities. Dan cleaned up 0.25 of the cities, David cleaned up 12 of
    10·1 answer
  • Five times a number is 30?
    12·2 answers
  • The net of a triangular prism is shown
    9·1 answer
  • Bank account A starts with $5,000 and grows by $1,000
    14·1 answer
  • 2.435 as a mixed number is
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!