P and Q are two rectangular containers. At first container P contained water to the height of 18.5 cm while that of container Q was 2 cm. The volume of water in container P was 1480 cm^3.

  1. (a)

    What was the base area of container P?

    Ans: (a) ___

  2. (b)

    Vera poured some water from container P into container Q without spilling. After that, the height of the water level of container P was the same as that of container Q. What was the new height of the water level in container Q?

    Ans: (b) ___

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Worked solution

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

Answer

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}

Answer

55 cm

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