## 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?

1. anonymous

@Michele_Laino

2. Michele_Laino

step #1 we have to compute the volume V of the spherical scoop: $\begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = ...? \hfill \\ \end{gathered}$

3. Michele_Laino

since if the diameter is 2.75 inches, then the radius is: 2.75/2=1.375 inches

4. anonymous

okay

5. anonymous

I got 2.374625

6. Michele_Laino

I got this: $\Large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered}$

7. Michele_Laino

$\large \begin{gathered} V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {1.375^3} = \hfill \\ \hfill \\ = \frac{{12.56}}{3} \times {1.375^3} = \frac{{12.56}}{3} \times 2.600 = 10.884inche{s^3} \hfill \\ \hfill \\ \end{gathered}$

8. anonymous

now I have to do the same for the cylindrical cup

9. Michele_Laino

yes!

10. Michele_Laino

the 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

11. Michele_Laino

I have used this approximation: pi = 3.14

12. Michele_Laino

what do you get?

13. anonymous

59.66

14. Michele_Laino

correct!

15. anonymous

sorry if Im going slow on the questions I writing the answers and work down

16. Michele_Laino

ok! no worries! :)

17. anonymous

I have to calculate the scoops

18. Michele_Laino

we can see that the cylindrical cup is too large since two scoops of ice occupy 10.884*2= 21.768 inches^3

19. anonymous

okay

20. anonymous

thank yu for helping me :D

21. Michele_Laino

:)

22. Michele_Laino

now we have to compute the volume of the cone shaped cup

23. anonymous

okay

24. anonymous

would is be 59.6 and 10.88

25. Michele_Laino

here is that volume: $\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = ...inche{s^3} \hfill \\ \end{gathered}$

26. Michele_Laino

since the radius is: 3.25/2= 1.625 inches

27. anonymous

okay

28. Michele_Laino

what do you get?

29. anonymous

1.625

30. Michele_Laino

that is the radius, whereas the volume is: $\begin{gathered} V = \frac{1}{3}3.14 \times R \times R \times H = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \hfill \\ \hfill \\ = \frac{{3.14 \times 1.625 \times 1.625 \times 3.75}}{3} = \frac{{3.14 \times 2.64 \times 3.75}}{3} = \hfill \\ \hfill \\ = 10.364inche{s^3} \hfill \\ \end{gathered}$

31. Michele_Laino

so the cone shaped cup is too small, since it can not contain 2 scoops of ice, therefore we have to choose the cylindrical cup