what is the diameter of a cone that has a volume of 56.52 cubic inches and a height of 6 inches. Use 3.14 for pi\",[{""content"":""<p><strong>Answer:<\/strong><\/p><p>The diameter of the cone with the given volume and height is <strong>equal to 6 inches<\/strong>.<\/p><p><strong>General Formulas and Concepts:<br \/><\/strong><u>Geometry<\/u><\/p><p>Volume of a Cone Formula: [tex]\\displaystyle V = \\frac{\\pi r^2 h}{3}[\/tex]<\/p><ul><li><em>r<\/em> is radius<\/li><li><em>h<\/em> is height<\/li><\/ul><p>Diameter of a Circle Formula: [tex]\\displaystyle d = 2r[\/tex]<\/p><ul><li><em>r<\/em> is radius<\/li><\/ul><p><strong>Step-by-step explanation:<\/strong><\/p><p><u>Step 1: Define<\/u><\/p><p><em>Identify variables.<\/em><\/p><p>[tex]\\displaystyle V = 56.52 \\ \\text{in}^3 \\\\h = 6 \\ \\text{in}[\/tex]<\/p><p><\/p><p><u>Step 2: Find Diameter<\/u><\/p><ol><li>[Volume of a Cone Formula] Substitute in variables:<br \/>[tex]\\displaystyle 56.52 \\ \\text{in}^3 = \\frac{\\pi r^2 (6 \\ \\text{in})}{3}[\/tex]<\/li><li>Solve for <em>r<\/em>:<br \/>[tex]\\displaystyle r = 3 \\ \\text{in}[\/tex]<\/li><li>[Diameter of a Circle Formula] Substitute in variables:<br \/>[tex]\\displaystyle d = 2(3 \\ \\text{in})[\/tex]<\/li><li>Evaluate:<br \/>[tex]\\displaystyle d = 6 \\ \\text{in}[\/tex]<\/li><\/ol><p>\u2234 we find the diameter to be <u>6 inches<\/u>.<\/p><p>---<\/p><p>Topic: Algebra I\/Geometry A<\/p>""}

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general 11 months ago 4163