A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
You are starting a Shaved Ice business and need to decide on a cup. Your choices are between a cone and a cylindrical shaped cup.
The cone shaped cup has a diameter of 3.25 inches and is 3.75 inches tall.
The cylindrical cup has a diameter of 4 inches and height of 4.75 inches.
The spherical scoop you have chosen has a diameter of 2.75 inches.
Which cup should you choose if you want two scoops of ice to best fit in the cup?
anonymous
 one year ago
You are starting a Shaved Ice business and need to decide on a cup. Your choices are between a cone and a cylindrical shaped cup. The cone shaped cup has a diameter of 3.25 inches and is 3.75 inches tall. The cylindrical cup has a diameter of 4 inches and height of 4.75 inches. The spherical scoop you have chosen has a diameter of 2.75 inches. Which cup should you choose if you want two scoops of ice to best fit in the cup?

This Question is Closed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0step #1 we have to compute the volume V of the spherical scoop: \[\begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = ...? \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0since if the diameter is 2.75 inches, then the radius is: 2.75/2=1.375 inches

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I got this: \[\Large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now I have to do the same for the cylindrical cup

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the volume V of the cylindrical cup is: \[\large \begin{gathered} V = 3.14 \times R \times R \times H = \hfill \\ \hfill \\ = 3.14 \times 2 \times 2 \times 4.75 = ...inche{s^3} \hfill \\ \end{gathered} \] since the radius is 4/2=2 inches

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I have used this approximation: pi = 3.14

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry if Im going slow on the questions I writing the answers and work down

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0ok! no worries! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have to calculate the scoops

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we can see that the cylindrical cup is too large since two scoops of ice occupy 10.884*2= 21.768 inches^3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank yu for helping me :D

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now we have to compute the volume of the cone shaped cup

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would is be 59.6 and 10.88

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0here is that volume: \[\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = ...inche{s^3} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0since the radius is: 3.25/2= 1.625 inches

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0that is the radius, whereas the volume is: \[\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = \hfill \\ \hfill \\ = 10.364inche{s^3} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so the cone shaped cup is too small, since it can not contain 2 scoops of ice, therefore we have to choose the cylindrical cup
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.