A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m…
2025
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
- A.
90 cm
- B.
1 dm
- C.
1 m
- D.
1.1 cm
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Correct answer: B
Let the thickness of the bottom be x cm.
External dimensions (in cm): 330 × 260 × 110
Internal length = 330 − 2×5 = 320 cm; internal width = 260 − 2×5 = 250 cm.
Internal height = 110 − x cm (bottom thickness is x cm).
Internal volume = 320 × 250 × (110 − x) cubic centimetres.
Set this equal to the required capacity: 8000 litres = 8,000,000 cm³.
So, 320 × 250 × (110 − x) = 8,000,000 ⇒ (110 − x) = 8,000,000 ÷ (320 × 250) = 100.
Therefore x = 110 − 100 = 10 cm = 1 decimetre (1 dm).