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Find the volume, the curved surface area and total surface area of a cone. given that(i) radius of base = 3.5 m and height = 12 m |
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Answer» Volume = 154 m³CSA of the cone = 137.5 m²TSA of the cone = 176 m²Step-by-step EXPLANATION:RADIUS = 3.5 mHeight = 12 mVolumeCurved surface areaTotal surface areaVolume of the cone:↠ The volume of a cone is given by the EQUATION, Volume of a cone = 1/3 × π × r² × h where r is the radius of the cone h is the height of the cone↠ Substitute the data, Volume of the cone = 1/3 × 22/7 × 3.5 × 3.5 × 12 Volume of the cone = 22 × 0.5 × 3.5 × 4 Volume of the cone = 154 m³↠ Hence volume of the cone is 154 m³.Curved surface area:↠ To find the CSA, we have to find the slant height of the cone.↠ The slant height of a cone is given by, Slant height = √(r² + h²)↠ Substituting the data, Slant height = √(3.5² + 12²) Slant height = √156.25 Slant height = 12.5 m↠ Now the CSA of a cone is given by, CSA of a cone = π r l where r is the radius and l is the slant height↠ Substituting the values, CSA of the cone = 22/7 × 3.5 × 12.5 CSA of the cone = 22 × 0.5 × 12.5 CSA of the cone = 137.5 m²↠ Hence curved surface area of the cone is 137.5 m².Total surface area:↠ The total surface area of a cone is given by, TSA of cone = π r (r + l)↠ Substitute the data, TSA of the cone = 22/7 × 3.5 (3.5 + 12.5) TSA of the cone = 22 × 0.5 × 16 TSA of the cone = 176 m²↠ Hence the total surface area of the cone is 176 m². |
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