This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back clever — been a while! Let's pick up where you left off. Step 1: Calculate the volume of the hemispherical pond. The pond is a hemisphere with a diameter of 12 m. The radius of the pond, r_p, is half of the diameter. r_p = (12)/(2) = 6 m The volume of a sphere is given by V = (4)/(3) r^3. Therefore, the volume of a hemisphere is half of that. (Note: The question states "Volume of sphere = (4)/(3) r^2", which appears to be a typo. We will use the correct formula for the volume of a sphere, V = (4)/(3) r^3.) The volume of the hemispherical pond, V_p, is: V_p = (1)/(2) × (4)/(3) r_p^3 = (2)/(3) r_p^3 Substitute r_p = 6 m and = 3.14: V_p = (2)/(3) × 3.14 × (6)^3 V_p = (2)/(3) × 3.14 × 216 V_p = 2 × 3.14 × (216)/(3) V_p = 2 × 3.14 × 72 V_p = 452.16 m^3 Step 2: Calculate the volume of water in the cylindrical tank. The water is poured into a cylindrical tank with a radius of 5 m. Let the height of the water in the tank be h. The radius of the cylindrical tank, r_t, is 5 m. The volume of a cylinder, V_t, is given by: V_t = r_t^2 h Substitute r_t = 5 m and = 3.14: V_t = 3.14 × (5)^2 × h V_t = 3.14 × 25 × h V_t = 78.5 h m^3 Step 3: Equate the volumes and solve for the height h. Since there is no loss of water, the volume of water from the pond is equal to the volume of water in the cylindrical tank: V_p = V_t 452.16 = 78.5 h Now, solve for h: h = (452.16)/(78.5) h ≈ 5.76 m The height of the water in the tank is approximately 5.76 m. The final answer is 5.76 m. Send me the next one 📸