A water bottle, which contains water, has a cylinder of radius 2 cm on top of another cylinder of radius 3 cm. When the bottle is upright, the height of the water is 3 cm, as shown in the cross-section of the bottle in Figure 1. When the bottle is upside down, the height of the liquid is 8 cm, as shown in Figure 2. What is the total height of the bottle in cm?
Explanation:
Let the total height of the bottle he H.
The empty volume in figure 1 = The empty volume in figure 2.
⇒ π × r2 × (H - 3) = π × R2 × (H - 8)
⇒ 22 × (H - 3) = 32 × (H - 8)
⇒ 4H - 12 = 9H - 72
⇒ 5H = 60
⇒ H = 12
Hence, option (c).
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