A spherical tank has a diameter of 10 meters. If it is filled to 80% of its capacity, what is the volume of water in the tank? Use \( \pi \approx 3.14 \).
["How to Calculate Water Volume in a Spherical Tank: A Practical Guide Using a 10-Meter Diameter Example", "When it comes to storing liquids, spherical tanks offer a space-efficient and robust solution. Understanding the volume of water they hold is crucial for industries like water supply, chemical storage, and oil refining. In this article, we explore a key calculation: what is the volume of water in a spherical tank with a 10-meter diameter filled to 80% of its capacity? We’ll break down the formula and walk you through the steps using real-world numbers and approximate values of ( \pi \approx 3.14 ).", "---", "### The Spherical Tank: Basics and Importance", "A spherical tank’s capacity depends on its diameter. Unlike cylinders or rectangles, spheres provide uniform stress distribution under pressure, making them ideal for high-pressure or corrosive liquid storage. The volume of a full spherical tank is calculated using the formula:", "[\nV_{\ ext{full}} = \frac{4}{3} \pi r^3\n]", "where ( r ) is the radius of the sphere. Since diameter equals twice the radius, a 10-meter diameter tank has a radius of 5 meters.", "---", "### Step 1: Calculate the Full Volume of the Tank", "Using ( r = 5 ) meters and ( \pi \approx 3.14 ):", "[\nV_{\ ext{full}} = \frac{4}{3} \ imes 3.14 \ imes (5)^3\n]", "First compute ( 5^3 = 125 ), then:", "[\nV_{\ ext{full}} = \frac{4}{3} \ imes 3.14 \ imes 125 = \frac{4}{3} \ imes 392.5 \approx \frac{1570}{3} \approx 523.33 \ ext{ cubic meters}\n]", "So, the full volume of the tank is approximately 523.33 m³.", "---", "### Step 2: Determine Volume at 80% Capacity", "Since the tank is filled to 80% of its total capacity, multiply the full volume by 0.80:", "[\nV_{80%} = 523.33 \ imes 0.80 \approx 418.67 \ ext{ cubic meters}\n]", "---", "### Summary", "- Diameter: 10 meters → Radius: 5 meters\n- Full volume: ~523.33 m³\n- Volume at 80% capacity: ~418.67 m³", "---", "### Why This Calculation Matters", "Knowing the exact water or liquid volume in a spherical tank supports efficient resource planning, maintenance scheduling, and disaster prevention in industrial settings. Whether for stormwater management, fuel storage, or emergency reserves, precise volume calculations ensure safety and reliability.", "---", "### Final Calculation Recap (using ( \pi \approx 3.14 )):", "[\nV_{\ ext{water}} = \frac{4}{3} \ imes 3.14 \ imes (5)^3 \ imes 0.8 = 418.67 \ ext{ m}^3\n]", "This shows a spherical tank with a 10-meter diameter holds roughly 418.67 cubic meters of water when filled to 80%.", "---", "Keywords: spherical tank volume, water volume in spherical tank, 10-meter diameter tank, 80% tank capacity, fluid storage calculation, π approximation, engineering example.", "---", "Stay informed, optimize storage, and maintain safety with precise volume calculations—starting with spherical tanks like this one."]
