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
nevsk [136]
1 year ago
9

Feeling anxious about another pandemic induced run-on toilet paper, Mrs. Phillips is making room in a closet for hording Angel S

oft toilet paper. Using the Fermi process, she wants to estimate the number of rolls of toilet paper she can fit into a rectangular section of a closet with dimensions of length 36 inches, width 36 inches, height 108 inches.
One Angel Soft MEGA roll has a diameter 5 inches, height 3.75 inches.

About how many Angel Soft MEGA rolls can be fit into the closet space?
Show all math work needed to complete this problem.
Mathematics
2 answers:
nevsk [136]1 year ago
5 0

Answer:

1372

Step-by-step explanation:

Rectangular closet dimensions:

  • length = 36 in
  • width = 36 in
  • height = 108 in

Modelling the roll of toilet paper as a cylinder with dimensions:

  • diameter = 5 in
  • height = 3.75 in

If we sit the rolls of toilet paper in the closet with their circular ends as their bases, then we can calculate the number of rolls that cover the base of the closet by dividing the length (and width) of the closet by the diameter of the toilet roll.

⇒ 36 in ÷ 5 in = 7.2 in

Therefore, we can fit 7 toilet rolls along the length and 7 toilet rolls along the width of the closet, meaning that we can fit 7 × 7 = 49 toilet rolls over the base of the closet.

Now calculate how many toilet rolls we can stack on top of each other.

To do this, divide the height of the closet by the height of the toilet roll:

⇒ 108 in ÷ 3.75 in = 28.8

Therefore, we can stack 28 layers of 49 toilet rolls in the closet.

So the total number of toilet rolls = 28 × 49 = 1372

There are other ways of stacking the toilet rolls in the closet (for example, turning them on their side), however, we cannot calculate the number of rolls the closet fits by simply dividing the volume of the closet space by the volume of a toilet roll, since the toilet rolls are cylinders and so there will always be some space between them.

romanna [79]1 year ago
3 0

For closet

It's a rectangle

  • L=36in
  • B=36in
  • H=108in

Volume

  • LBH
  • 36²(108)
  • (36)³(3)
  • 139968in³

For rolls:-

Cylindrical body

  • radius=r=5/2=2.5in
  • Height=h=3.75in

Volume:-

  • πr²h
  • π(2.5)²(3.75)
  • π(6.25)(3.75)
  • 73.6in³

Total rolls:-

  • Volume of closet /Volume of rolls
  • 139968/73.6
  • 1901.7
  • 1902 rolls
You might be interested in
What would you have to do to change 10 cubic feet into cubic inches?
Alina [70]

A. Divide by 46,656

B. Multiply by 1,728

C. Divide by 1,728

D. Multiply by 46,656

THE ANSWER IS B MULTIPLY BY 1,728


5 0
3 years ago
Can anyone explain how to awnser -72/7 × -48/11?
kkurt [141]
Maybe search up Algebra calculator and type in the equation? idk
8 0
3 years ago
If two water towers can hold 905 gallons of water, how much water can 11 water towers can hold
KonstantinChe [14]

Answer:

4977.5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Help i want help plz help me
sergejj [24]

Answer:

SA = 384 in ^2

Step-by-step explanation:

The surface area of a cube is given by

SA = 6 S ^2 where s is the side length

SA = 6 * (8) ^2

SA = 6 * 64

SA = 384 in ^2

7 0
3 years ago
Read 2 more answers
100 points! simplify write as a product compute
Rom4ik [11]

Answer:

a) \sqrt{61 - 24 \sqrt{5} }  =  - 4  + 3 \sqrt{5}

b)( \sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) }  + {2 \sqrt{bc}  } )

c) \frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }  =   - 1

Step-by-step explanation:

We want to simplify

\sqrt{61 - 24 \sqrt{5} }

Let :

\sqrt{61 - 24 \sqrt{5} }  = a - b \sqrt{5}

Square both sides of the equation:

(\sqrt{61 - 24 \sqrt{5} } )^{2}  =  ({a - b \sqrt{5} })^{2}

Expand the RHS;

61 - 24 \sqrt{5} =  {a}^{2}  - 2ab \sqrt{5}  + 5 {b}^{2}

Compare coefficients on both sides:

{a}^{2}  + 5 {b}^{2}  = 61 -  -  - (1)

- 24 =  - 2ab \\ ab = 12 \\ b =  \frac{12}{b}  -  -  -( 2)

Solve the equations simultaneously,

\frac{144}{ {b}^{2} }  + 5 {b}^{2}  = 61

5 {b}^{4}  - 61 {b}^{2}  + 144 = 0

Solve the quadratic equation in b²

{b}^{2}  = 9 \: or \:  {b}^{2}  =  \frac{16}{5}

This implies that:

b =  \pm3 \: or \: b =  \pm  \frac{4 \sqrt{5} }{5}

When b=-3,

a =  - 4

Therefore

\sqrt{61 - 24 \sqrt{5} }  =  - 4  + 3 \sqrt{5}

We want to rewrite as a product:

{b}^{2}  {c}^{2}  - 4bc -  {b}^{2}  -  {c}^{2}  + 1

as a product:

We rearrange to get:

{b}^{2}  {c}^{2}   -  {b}^{2}  -  {c}^{2}  + 1- 4bc

We factor to get:

{b}^{2} ( {c}^{2}   -  1)  -  ({c}^{2}   -  1)- 4bc

Factor again to get;

( {c}^{2}   -  1) ({b}^{2}   -  1)- 4bc

We rewrite as difference of two squares:

(\sqrt{( {c}^{2}   -  1) ({b}^{2}   -  1) })^{2} - ( {2 \sqrt{bc} })^{2}

We factor the difference of square further to get;

( \sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2}   -  1) ({b}^{2}    -  1) }  + {2 \sqrt{bc}  } )

c) We want to compute:

\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }

Let the numerator,

\sqrt{9 - 4 \sqrt{5} }  = a - b \sqrt{5}

Square both sides of the equation;

9 - 4 \sqrt{5}  =  {a}^{2}  - 2ab \sqrt{5}  + 5 {b}^{2}

Compare coefficients in both equations;

{a}^{2}  + 5 {b}^{2}  = 9 -  -  - (1)

and

- 2ab =  - 4 \\ ab = 2 \\ a =  \frac{2}{b}  -  -  -  - (2)

Put equation (2) in (1) and solve;

\frac{4}{ {b}^{2} }  + 5 {b}^{2}  = 9

5 {b}^{4}   - 9 {b}^{2}  + 4 = 0

b =  \pm1

When b=-1, a=-2

This means that:

\sqrt{9 - 4 \sqrt{5} }  =  - 2 +  \sqrt{5}

This implies that:

\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 -  \sqrt{5} }  =  \frac{ - 2 +  \sqrt{5} }{2 -  \sqrt{5} }  =  \frac{ - (2 -  \sqrt{5)} }{2 -  \sqrt{5} }  =  - 1

3 0
3 years ago
Read 2 more answers
Other questions:
  • Is 2/7 greater than 4/21
    6·2 answers
  • A standard deck of playing cards contains 52 cards, equally divided among four suits (hearts, diamonds, clubs, and spades). Each
    15·1 answer
  • If ΔABC ΔDEC, what is m∠D? A. 40° B. 150° C. 60° D. 80°
    15·1 answer
  • How do you solve this
    8·1 answer
  • The lung capacity of the blue whale is 5100L. Convert this volume into gallons. Express your answer to two significant figures a
    9·1 answer
  • If question 7, how do you solve for the angles
    9·1 answer
  • A half-circle is joined to an equilateral triangle with side lengths of 12 units. What is the perimeter of the resulting shape?
    5·1 answer
  • Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2 feet. What is the total length
    9·1 answer
  • Drag each equation to the correct location on the table.
    9·1 answer
  • 18 is 4.5 times a number.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!