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

### Concept & Internal Capacity of a Cistern The internal capacity (volume) is found using the internal dimensions. 1 litre equals 1000 cm$^3$. $$ \text{Capacity} = l \times b \times h $$ ### Step-by-Step Solution 1. **Given:** External dimensions: $L = 3.3$ m $= 330$ cm, $B = 2.6$ m $= 260$ cm, $H = 1.1$ m $= 110$ cm. Wall thickness $t = 5$ cm. Capacity = 8000 litres. 2. **Convert Capacity to cm$^3$:** $$ 8000 \text{ L} = 8000 \times 1000 = 8000000 \text{ cm}^3 $$ 3. **Calculate Internal Length and Breadth:** $l = 330 - 2(5) = 320$ cm. $b = 260 - 2(5) = 250$ cm. 4. **Calculate Internal Height ($h$):** $$ l \times b \times h = 8000000 $$ $$ 320 \times 250 \times h = 8000000 $$ $$ 80000h = 8000000 \implies h = 100 \text{ cm} $$ 5. **Determine Bottom Thickness:** A cistern is open at the top. The difference between external and internal height represents the thickness of the bottom. Bottom thickness = $H - h = 110 - 100 = 10$ cm. 6. **Convert Units:** 10 cm equals 1 decimeter (dm). ### Exam Strategy & Shortcut Recognize that a cistern is typically open at the top, which means only the bottom contributes to the height difference. ### Common Pitfall Assuming the cistern is a closed tank and setting the bottom thickness to half the difference of the heights. ### Final Answer Therefore, the correct answer is **1 dm**.