A cylindrical tank with a radius of 3 meters and a height of 10 meters is filled with water. Calculate the volume of water in the tank in cubic meters. Use π ≈ 3.14.
["# Calculating the Volume of Water in a Cylindrical Tank", "Storing water efficiently is crucial in various industrial, agricultural, and municipal applications. One common solution is the cylindrical water tank, known for its durability and space-saving design. Today, we explore a cylindrical tank with a radius of 3 meters and a height of 10 meters filled completely with water, calculating its total volume in cubic meters using the formula for a cylinder’s volume.", "## Understanding the Cylinder Volume Formula", "The volume ( V ) of a cylinder is calculated using the formula:", "[\nV = \pi r^2 h\n]", "Where:\n- ( r ) = radius of the cylinder’s base (in meters)\n- ( h ) = height of the cylinder (in meters)\n- ( \pi ) ≈ 3.14 (standard approximation)", "This formula describes how much space the tank occupies when filled, which directly correlates to the volume of water it contains.", "## Applying the Given Dimensions", "For the tank analyzed:\n- Radius ( r = 3 ) meters\n- Height ( h = 10 ) meters", "Now substitute these values into the volume formula:", "[\nV = 3.14 \ imes (3)^2 \ imes 10\n]", "First, calculate the square of the radius:", "[\n3^2 = 9\n]", "Then multiply by height and π:", "[\nV = 3.14 \ imes 9 \ imes 10 = 3.14 \ imes 90\n]", "[\nV = 282.6\n]", "## Final Volume in Cubic Meters", "The cylindrical tank holds exactly 282.6 cubic meters of water when fully filled. This precise calculation ensures accurate planning for water supply, storage capacity, or system sizing.", "Using this formula and values, engineers and project managers can easily estimate tank capacity and optimize water resources for residential, commercial, or industrial use.", "### Summary", "- Tank radius: 3 meters\n- Tank height: 10 meters\n- Filled volume: 282.6 m³\n- Formula: ( V = \pi r^2 h )\n- π ≈ 3.14", "This cylindrical tank represents a reliable and efficient solution for water storage, backed by clear and reliable mathematical standards."]
