Question

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? 

Answer 1

@Michele_Laino

Answer 2

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

Answer 3

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

Answer 4

okay

Answer 5

I got 2.374625

Answer 6

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

Answer 7

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

Answer 8

now I have to do the same for the cylindrical cup

Answer 9

yes!

Answer 10

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

Answer 11

I have used this approximation:
pi = 3.14

Answer 12

what do you get?

Answer 13

59.66

Answer 14

correct!

Answer 15

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

Answer 16

ok! no worries! :)

Answer 17

I have to calculate the scoops

Answer 18

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

Answer 19

okay

Answer 20

thank yu for helping me :D

Answer 21

:)

Answer 22

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

Answer 23

okay

Answer 24

would is be 59.6 and 10.88

Answer 25

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

Answer 26

since the radius is:
3.25/2= 1.625 inches

Answer 27

okay

Answer 28

what do you get?

Answer 29

1.625

Answer 30

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

Answer 31

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