图中显示了两套几何相似的杯碟组合。较小碟子的直径为 5 cm。较大碟子的直径为 6.5 cm。一家咖啡店以 $1 的价格出售较小杯咖啡，以 $2 的价格出售较大杯咖啡。计算哪一种更划算。解释你的答案。答案 ...

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Find the linear scale factor from the smaller set to the larger set.

$\text{Linear scale factor}=\frac{6.5}{5}=1.3$

2. Find the volume scale factor for the coffee cups.

Since the cup-and-saucer sets are geometrically similar, volumes scale by the cube of the linear scale factor.

$\text{Volume scale factor}=1.3^3=2.197$

So the larger cup holds $2.197$ times as much coffee as the smaller cup.

3. Compare the price scale factor with the volume scale factor.

$\text{Price scale factor}=\frac{\$2}{\$1}=2$

The larger cup costs $2$ times as much, but gives $2.197$ times as much coffee.

4. Decide which cup gives better value for money and explain.

Since $2.197>2$ , the increase in coffee is greater than the increase in price.

Therefore, the larger cup gives more coffee per dollar.

答案

The larger cup is the better buy, since it holds about $2.197$ times as much coffee but costs only $2$ times as much.

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