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
Fynjy0 [20]
1 year ago
14

The manufacturing engineers of a renowned pizza brand reduced the manufacturing cost of a pizza delivery box by optimising the s

hape of the box.To achieve this cost optimisation, the engineers reduced the volume of the box by 25% by flattening the curved side of the box (illustrated by the dashed line) to shape it like a proper prism, as shown in the below diagram.24 cm2836 cm(a) Find the value of 20.(b) (i) Find the area of the sector of the top surface of the old box design:(ii) Find the area of the top surface of the newly designed box.If the volume of the old box design was 3277 cm³, find the volume, V, of the newly designed box. rounding your answer correct to the nearest cubic centimetre:(ii) Hence, find the value of h.

Mathematics
1 answer:
jekas [21]1 year ago
8 0

Given: A pizza box's volume has been reduced by 25% by flattening the curved side of the box. The dimensions of the box are given.

Required: To determine the angle, the area of the sector of the top surface of the old box design, the area of the top surface of the newly designed box, and the volume, V, of the newly designed box. Also, determine the height of the box, h.

Explanation: The given box is-

If we draw a perpendicular as shown in the figure, the angle is bisected, and the side 24 cm is also bisected as the triangle on the top is an isosceles triangle. This can be easily proved by showing that the smaller triangles on the top face are congruent.

Next, we can use the trigonometric ratio sine to determine the angle as follows-

\begin{gathered} sin\theta=\frac{12}{36} \\ \theta=sin^{-1}(\frac{1}{3}) \\ \theta=19.47\degree \end{gathered}

Thus,

2\theta=38.94\degree

Next, the top of the new box is now a triangle with a base of 24 cm and a height-

\begin{gathered} \text{ Height of triangle}=36cos\theta \\ =36cos(19.47\degree) \\ =33.94\text{ cm} \end{gathered}

Hence, the area is-

\begin{gathered} A=\frac{1}{2}\times24\times33.94 \\ =407.30\text{ cm}^2 \end{gathered}

Now, the old box is a sector with a central angle of 38.94 degrees and a radius of 36 cm. Hence the area of the old box is-

\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\  \end{gathered}

Substituting the values as-

\begin{gathered} A=\frac{38.94}{360}\times3.14\times36\times36 \\ =440.18\text{ cm}^2 \end{gathered}

Lastly, the volume of the new box is 25% less than the old box. Hence the volume of the new box is-

\begin{gathered} V=\frac{25}{100}\times3277 \\ =819.25\text{ cm}^3 \end{gathered}

We can determine the height as follows-

\begin{gathered} Vol=Area\times h \\ \Rightarrow h=\frac{Vol}{Area} \end{gathered}

Hence,

\begin{gathered} h=\frac{819.25}{407.30} \\ =2.011\text{ cm} \end{gathered}

Final Answer: A)

2\theta=38.94\degree

B) i) The area of the top of the old box=440.18 sq centimeters.

ii) The area of the top of the new box=407.30 sq centimeters.

C) i) The volume of the new box is 819 cubic centimeters.

ii) h=2.01 cm

You might be interested in
PJ is Decorating Pupcakes for Rocky´s Birthday Party. Her Color Scheme is Black, Purple, and Green. She Will use This Spinner to
Veseljchak [2.6K]

Answer:

173

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A baker uses 4 cups of flour for each cake. He has 213 cups of flour in his shop. How many cakes can he make, and how much flour
lora16 [44]
<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Just divide the values:

213 / 4 = 53.25

He can make 53 cakes.

53 x 4 = 212

Subtract this from the original:

213 - 212 = 1

1 cup of flour is left over

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

8 0
3 years ago
Polynomial of degree 4 has 1 positive real root that is bouncer and 1 negative real root that is a bouncer. How many imaginary r
Rainbow [258]

Answer:

<h3>The given polynomial of degree 4 has atleast one imaginary root</h3>

Step-by-step explanation:

Given that " Polynomial of degree 4 has 1 positive real root that is bouncer and 1 negative real root that is a bouncer:

<h3>To find how many imaginary roots does the polynomial have :</h3>
  • Since the degree of given polynomial is 4
  • Therefore it must have four roots.
  • Already given that the given polynomial has 1 positive real root and 1 negative real root .
  • Every polynomial with degree greater than 1  has atleast one imaginary root.
<h3>Hence the given polynomial of degree 4 has atleast one imaginary root</h3><h3> </h3>

8 0
3 years ago
Angle m AOC=108° m AOB=3x+4° m BOC=8x-28°<br><br> Find m AOB
Alex787 [66]

Hello from MrBillDoesMath!

Answer:

40



Discussion:

A diagram is always appreciated!

Assuming that

mAOC = mAOB    + mBOC       =>

108      = (3x + 4)  +  (8x - 28)    =>  combine common terms

108      = (3x + 8x) + (4 - 28 )     =>

108      = 11x - 24                        =>   add 24 to both sides

132     = 11x                                 =>

x = 132/11 = 12


So mAOB = 3x + 4 = 3(12) + 4 = 36 + 4 = 40



Thank you,

MrB

4 0
3 years ago
-1/2 + (3/4 x 4/9) =
Nookie1986 [14]
-.1666667
You can use khan academy or Socratic if you still not sure.
7 0
3 years ago
Other questions:
  • Find a non-zero, two-by-two matrix such that:
    13·1 answer
  • Ruiz needs to buy a countertop for a kitchen. He calculated the area to be 16 square feet. The actual area is 15.4 square feet.
    5·2 answers
  • Please can someone show me how to do this. Thanks
    15·1 answer
  • I wished I’d bought the game last week for $199.00. I missed the sale, and now it’s an additional 25%. What will it cost me now
    7·1 answer
  • Which problem situation best matches the equation 10 + 2x = 16?
    15·2 answers
  • What is 115/5-60/20
    15·1 answer
  • What is the final result when either algebraic or numerical fractions are added together?
    14·2 answers
  • Simplify 3^5 please for 10 points
    6·2 answers
  • Also this pls pls pls
    12·1 answer
  • 2 [32-(4-1) power of 3
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!