Subjects MATHEMATICS

Capacity And Volume

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Capacity And Volume


1. The problem asks to find the depth of remaining water in a water tank with a square base 3m by 3m and holding 22500L when full, after removing 4500L. 2. First, convert capacity from liters to cubic meters: since 1L = 0.001m³, total volume when full is $$22500 \times 0.001 = 22.5\, m^3$$. 3. The base area of the tank is $$3m \times 3m = 9\, m^2$$. 4. Calculate the height when full: $$\text{Height}_{full} = \frac{\text{Volume}_{full}}{\text{Base area}} = \frac{22.5}{9} = 2.5\, m$$. 5. Water drawn off is 4500L, convert to cubic meters: $$4500 \times 0.001 = 4.5\, m^3$$. 6. Remaining volume is $$22.5 - 4.5 = 18\, m^3$$. 7. Calculate remaining depth: $$\text{Depth}_{remaining} = \frac{\text{Remaining volume}}{\text{Base area}} = \frac{18}{9} = 2\, m$$. **Answer:** The depth of remaining water is 2 meters. --- 1. The problem asks to find the height of a cylindrical container of diameter 7cm and volume 385cm³, using $$\pi=\frac{22}{7}$$. 2. The cylinder's volume formula is $$V = \pi r^2 h$$. 3. Calculate radius: $$r = \frac{diameter}{2} = \frac{7}{2} = 3.5\, cm$$. 4. Rearrange to find height: $$h = \frac{V}{\pi r^2}$$. 5. Compute $$r^2 = (3.5)^2 = 12.25$$. 6. Substitute values: $$h = \frac{385}{\frac{22}{7} \times 12.25} = \frac{385}{\frac{22}{7} \times 12.25}$$. 7. Calculate denominator: $$\frac{22}{7} \times 12.25 = \frac{22 \times 12.25}{7} = \frac{269.5}{7} = 38.5$$. 8. Final height calculation: $$h = \frac{385}{38.5} = 10\, cm$$. **Answer:** The height of the cylinder is 10 cm.