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### Mensuration of a Cylinder: Volume, Total Surface Area, Hollow Cylinders

 A solid cylinder has height 16 inches and radius 10 inches. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 102 x 16 = 5026.55 cubic inches Curved Surface Area = 2 x Π x radius x height = 1005.31 square inches Surface Area of each circular end = Π x Radius2 = π x 102 = 314.16 square inches Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 1633.63 square inches A solid cylinder has height 20 cm and radius 3 cm. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 32 x 20 = 565.49 cubic cm Curved Surface Area = 2 x Π x radius x height = 376.99 square cm Surface Area of each circular end = Π x Radius2 = π x 32 = 28.27 square cm Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 433.54 square cm A solid cylinder has height 12 m and radius 20 m. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 202 x 12 = 15079.64 cubic m Curved Surface Area = 2 x Π x radius x height = 1507.96 square m Surface Area of each circular end = Π x Radius2 = π x 202 = 1256.64 square m Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 4021.24 square m A solid cylinder has height 1 units and radius 4 units. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 42 x 1 = 50.27 cubic units Curved Surface Area = 2 x Π x radius x height = 25.13 square units Surface Area of each circular end = Π x Radius2 = π x 42 = 50.27 square units Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 125.66 square units A solid cylinder has height 2 inches and radius 5 inches. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 52 x 2 = 157.08 cubic inches Curved Surface Area = 2 x Π x radius x height = 62.83 square inches Surface Area of each circular end = Π x Radius2 = π x 52 = 78.54 square inches Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 219.91 square inches A solid cylinder has height 11 cm and radius 13 cm. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 132 x 11 = 5840.22 cubic cm Curved Surface Area = 2 x Π x radius x height = 898.5 square cm Surface Area of each circular end = Π x Radius2 = π x 132 = 530.93 square cm Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 1960.35 square cm A solid cylinder has height 4 m and radius 15 m. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 152 x 4 = 2827.43 cubic m Curved Surface Area = 2 x Π x radius x height = 376.99 square m Surface Area of each circular end = Π x Radius2 = π x 152 = 706.86 square m Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 1790.71 square m A solid cylinder has height 16 units and radius 2 units. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 22 x 16 = 201.06 cubic units Curved Surface Area = 2 x Π x radius x height = 201.06 square units Surface Area of each circular end = Π x Radius2 = π x 22 = 12.57 square units Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 226.19 square units A solid cylinder has height 6 inches and radius 14 inches. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 142 x 6 = 3694.51 cubic inches Curved Surface Area = 2 x Π x radius x height = 527.79 square inches Surface Area of each circular end = Π x Radius2 = π x 142 = 615.75 square inches Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 1759.29 square inches A solid cylinder has height 11 cm and radius 8 cm. What is the volume and total surface area of the cylinder? Volume = Π x Radius2 x Height = Π x 82 x 11 = 2211.68 cubic cm Curved Surface Area = 2 x Π x radius x height = 552.92 square cm Surface Area of each circular end = Π x Radius2 = π x 82 = 201.06 square cm Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 955.04 square cm A hollow cylinder has height 10 inches and outer radius R=17 inches and inner radius r=16 inches. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (172 - 162) x 10 = 1036.73 cubic inches A hollow cylinder has height 4 cm and outer radius R=18 cm and inner radius r=16 cm. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (182 - 162) x 4 = 854.51 cubic cm A hollow cylinder has height 7 m and outer radius R=23 m and inner radius r=22 m. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (232 - 222) x 7 = 989.6 cubic m A hollow cylinder has height 1 units and outer radius R=15 units and inner radius r=13 units. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (152 - 132) x 1 = 175.93 cubic units A hollow cylinder has height 15 inches and outer radius R=14 inches and inner radius r=12 inches. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (142 - 122) x 15 = 2450.44 cubic inches A hollow cylinder has height 3 cm and outer radius R=11 cm and inner radius r=9 cm. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (112 - 92) x 3 = 376.99 cubic cm A hollow cylinder has height 20 m and outer radius R=10 m and inner radius r=8 m. What is the volume of the cylinder? Volume = Π x (R2 - r2) x Height = Π x (102 - 82) x 20 = 2261.95 cubic m A solid cylinder has volume 26464.78 cubic inches and radius 18 inches. What is the total surface area of the cylinder? Since we have been given the volume and the radius, we need to compute the height first. Volume = Π x Radius2 x Height => Height = Volume/(Π x Radius2) = 26 inches Curved Surface Area = 2 x Π x radius x height = 2940.53 square inches Surface Area of each circular end = Π x Radius2 = π x 182 = 1017.88 square inches Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 4976.28 square inches A solid cylinder has volume 1884.96 cubic cm and radius 5 cm. What is the total surface area of the cylinder? Since we have been given the volume and the radius, we need to compute the height first. Volume = Π x Radius2 x Height => Height = Volume/(Π x Radius2) = 24 cm Curved Surface Area = 2 x Π x radius x height = 753.98 square cm Surface Area of each circular end = Π x Radius2 = π x 52 = 78.54 square cm Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 911.06 square cm A solid cylinder has volume 10643.72 cubic m and radius 11 m. What is the total surface area of the cylinder? Since we have been given the volume and the radius, we need to compute the height first. Volume = Π x Radius2 x Height => Height = Volume/(Π x Radius2) = 28 m Curved Surface Area = 2 x Π x radius x height = 1935.22 square m Surface Area of each circular end = Π x Radius2 = π x 112 = 380.13 square m Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 2695.49 square m A solid cylinder has volume 16342.56 cubic units and radius 17 units. What is the total surface area of the cylinder? Since we have been given the volume and the radius, we need to compute the height first. Volume = Π x Radius2 x Height => Height = Volume/(Π x Radius2) = 18 units Curved Surface Area = 2 x Π x radius x height = 1922.65 square units Surface Area of each circular end = Π x Radius2 = π x 172 = 907.92 square units Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 3738.5 square units A solid cylinder has volume 8004.78 cubic inches and height 14 inches. What is the total surface area of the cylinder? Volume = Π x Radius2 x Height => Radius = √(V/Πh) = 14 inches Curved Surface Area = 2 x π x radius x height = 1143.54 square inches Surface Area of each circular end = Π x Radius2 = π x 142 = 615.75 square inches Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 2375.04 square inches A solid cylinder has volume 11309.73 cubic cm and height 15 cm. What is the total surface area of the cylinder? Volume = Π x Radius2 x Height => Radius = √(V/Πh) = 15 cm Curved Surface Area = 2 x π x radius x height = 1507.96 square cm Surface Area of each circular end = Π x Radius2 = π x 152 = 706.86 square cm Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 2921.68 square cm A solid cylinder has volume 8743.05 cubic m and height 11 m. What is the total surface area of the cylinder? Volume = Π x Radius2 x Height => Radius = √(V/Πh) = 11 m Curved Surface Area = 2 x π x radius x height = 1589.65 square m Surface Area of each circular end = Π x Radius2 = π x 112 = 380.13 square m Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 2349.91 square m A solid cylinder has volume 2280.8 cubic units and height 11 units. What is the total surface area of the cylinder? Volume = Π x Radius2 x Height => Radius = √(V/Πh) = 11 units Curved Surface Area = 2 x π x radius x height = 414.69 square units Surface Area of each circular end = Π x Radius2 = π x 112 = 380.13 square units Total Surface Area of the cylinder = Curved Surface Area + 2 x (Surface area of each circular end) = 1174.96 square units