P和Q是两个长方体容器。起初,容器P中水的高度为18.5 cm,而容器Q中水的高度为2 cm。容器P中水的体积为1480 cm^3。

  1. (a)

    容器P的底面积是多少?

    答: (a) ___

  2. (b)

    Vera将容器P中的一些水倒入容器Q中,没有溢出。之后,容器P的水位高度与容器Q的水位高度相同。容器Q中新的水位高度是多少?

    答: (b) ___

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完整解法

15(a)

1. Calculate the base area of container P using its volume and height

Base Area=VolumeHeight=148018.5=80 cm2\text{Base Area} = \frac{\text{Volume}}{\text{Height}} = \frac{1480}{18.5} = 80\text{ cm}^2

答案

80 cm280\text{ cm}^2

15(b)

1. Find the base area of container P (from part a)

Base area of P =1480÷18.5=80 cm2= 1480 \div 18.5 = 80 \text{ cm}^2

2. Find the base area of container Q

Base area of Q =40×9=360 cm2= 40 \times 9 = 360 \text{ cm}^2

3. Find the total volume of water in both containers

Initial volume in Q =360×2=720 cm3= 360 \times 2 = 720 \text{ cm}^3
Total volume =1480+720=2200 cm3= 1480 + 720 = 2200 \text{ cm}^3

4. Find the new common height

Total base area =80+360=440 cm2= 80 + 360 = 440 \text{ cm}^2
New height =Total volumeTotal base area=2200440=5 cm= \frac{\text{Total volume}}{\text{Total base area}} = \frac{2200}{440} = 5 \text{ cm}

答案

55 cm

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