Glass label paper

We want to stick labels on the glasses. The labels stick right around the glass.
The diameter of the cup is 6 cm.
The height of the label is 10 cm.
a) How many labels will we make from 30 x 40 cm paper?
b) How many papers of this size will we use to make 100 labels?

Final Answer:

a =  6
b =  17

Step-by-step explanation:

$$\begin{gathered} d=6\text{cm} \\ h=10\text{cm} \\ x=30\text{cm} \\ y=40\text{cm} \\ L=\pi \cdot d=3.1416\cdot 6\doteq 18.8496\text{cm} \\ {S}_1=L\cdot h=18.8496\cdot 10\doteq 188.4956{\text{cm}}^2 \\ {S}_2=x\cdot y=30\cdot 40=1200{\text{cm}}^2 \\ a=\lfloor S_2/S_1\rfloor =\lfloor 1200/188.4956\rfloor =6 \end{gathered}$$

$$\begin{gathered} n_2=100/6=\frac{50}{3}=16\frac{2}{3}\doteq 16.6667 \\ b=\lceil n_2\rceil =\lceil 16.6667\rceil =17 \end{gathered}$$

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