1. **Problem statement:** We have a toilet tank with two flush buttons, A and B. Button A empties the entire tank, and button B empties the tank only up to a dotted line inside the tank. The tank refills at a rate of 3.6 liters per minute. 2. **Given data:** - Button A empties the tank in 6 seconds. - Refill rate: 3.6 liters/minute. - Dimensions from the figure (converted to meters): - Top length = 14 cm = 0.14 m - Slant length = 40 cm = 0.40 m - Left height = 24 cm = 0.24 m - Right height total = 10 cm + 7 cm = 17 cm = 0.17 m - Dotted line height = 7 cm = 0.07 m 3. **Step a: Calculate the total volume of the tank and refill time after pressing button A** - The tank shape is a trapezoidal prism. The cross-sectional area is trapezoid with bases 0.24 m and 0.17 m, and height 0.40 m. - Area of trapezoid cross-section: $$ A = \frac{(0.24 + 0.17)}{2} \times 0.40 = \frac{0.41}{2} \times 0.40 = 0.205 \times 0.40 = 0.082 \text{ m}^2 $$ - Volume of tank: $$ V = A \times \text{length} = 0.082 \times 0.14 = 0.01148 \text{ m}^3 $$ - Convert volume to liters (1 m³ = 1000 liters): $$ V = 0.01148 \times 1000 = 11.48 \text{ liters} $$ - Refill rate is 3.6 liters/minute, so refill time: $$ t = \frac{11.48}{3.6} = 3.19 \text{ minutes} $$ - Laju penurunan air (rate of water decrease) when button A is pressed for 6 seconds: $$ \text{Rate} = \frac{11.48 \text{ liters}}{6 \text{ seconds}} = 1.913 \text{ liters/second} $$ 4. **Step b: Calculate volume of water released when button B is pressed (up to dotted line)** - Height of water released is from 0.07 m to 0.24 m on left side and 0.07 m to 0.10 m on right side (since total right height is 0.17 m, dotted line is at 0.07 m, so water above dotted line is 0.10 m on right side). - Heights for trapezoid cross-section for button B flush: - Left base = 0.24 - 0.07 = 0.17 m - Right base = 0.10 m - Height (length) = 0.40 m - Area of trapezoid cross-section for button B flush: $$ A_B = \frac{(0.17 + 0.10)}{2} \times 0.40 = \frac{0.27}{2} \times 0.40 = 0.135 \times 0.40 = 0.054 \text{ m}^2 $$ - Volume for button B flush: $$ V_B = A_B \times 0.14 = 0.054 \times 0.14 = 0.00756 \text{ m}^3 $$ - Convert to cubic meters: $$ V_B = 0.00756 \text{ m}^3 $$ 5. **Step c: Calculate total water volume released for 15 flushes with ratio A:B = 2:1** - Total flushes = 15 - Number of A flushes: $$ n_A = \frac{2}{3} \times 15 = 10 $$ - Number of B flushes: $$ n_B = \frac{1}{3} \times 15 = 5 $$ - Total volume released: $$ V_{total} = n_A \times 11.48 + n_B \times (0.00756 \times 1000) $$ $$ V_{total} = 10 \times 11.48 + 5 \times 7.56 = 114.8 + 37.8 = 152.6 \text{ liters} $$ **Final answers:** - a. Refill time after button A flush: **3.19 minutes** - a. Rate of water decrease when button A pressed: **1.913 liters/second** - b. Volume of water released by button B flush: **0.00756 m³** - c. Total water released for 15 flushes with ratio 2:1: **152.6 liters**