Ice cream cone

How many cm² of dough are needed to produce an ice cream cone if it is to hold 0.3 l of ice cream and its
height is to be 15 cm. Add 8% for folds.

1. Convert litres into cm³
2. Decide which data you can calculate first and from what formula.
3. Calculate the data from point 2.
4. Write the formula for calculating … and sketch the triangle from which you calculate the missing dimension.
5. Calculate the dimension from point 4.
6. Calculate how many cm² will be needed to produce the cone (including 8% for folds).

Final Answer:

S =  17.2 cm²

Step-by-step explanation:

$$\begin{gathered} V=0.3\text{l}\to {\text{cm}}^3=0.3\cdot 1000{\text{cm}}^3=300{\text{cm}}^3 \\ h=15\text{cm} \\ p=8\%=\frac{8}{100}=\frac{2}{25}=0.08 \\ V=S_{1}h/3 \\ {S}_1=\frac{3\cdot V}{h}=\frac{3\cdot 300}{15}=60{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1/\pi }=\sqrt{60/3.1416}\doteq 4.3702\text{cm} \\ s=\sqrt{h^2+r^2}=\sqrt{15^2+4.3702^2}\doteq 15.6237\text{cm} \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 4.3702\cdot 15.6237\doteq 214.5029{\text{cm}}^2 \\ S=p\cdot S_2=0.08\cdot 214.5029=17.2{\text{cm}}^2 \end{gathered}$$

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