A cylinder, 20 cm long, 5 cm long is cut off, the surface area of the cylinder is reduced by 31.4 square centimeters, the volume of the original cylinder

A cylinder, 20 cm long, 5 cm long is cut off, the surface area of the cylinder is reduced by 31.4 square centimeters, the volume of the original cylinder

Perimeter of bottom surface: 31.4 △ 5 = 6.28 (CM)
Bottom area: 3.14 × (6.28 △ 3.14 △ 2) ^ 2 = 3.14 (square centimeter)
Side area: 6.28 × 20 = 125.6 (cm2)
Surface area: 125.6 + 3.14 × 2 = 131.88 (cm2)

As shown in the figure, after a cylinder is cut off 5cm, the surface area of the cylinder is reduced by 31.4cm2

Bottom circumference: 31.4 △ 5 = 6.28 (CM), bottom radius: 6.28 △ 3.14 △ 2 = 1 (CM), two bottom areas: 3.14 × 12 × 2 = 6.28 (cm 2), side area: 6.28 × 20 = 125.6 (cm 2), surface area: 125.6 + 6.28 = 131.88 (cm 2). Answer: the surface area of the original cylinder is 131.88 cm 2

Use a cube with a surface area of 180 square centimeters to cut it into the largest cylinder and calculate the surface area of the cylinder

180 / 6 = 30 square centimeter
Let the radius of the cylinder be r, then (2R) &# 178; = 30, 2R = radical 30, R & # 178; = 15 / 2
Surface area = 2 * π * 15 / 2 + radical 30 π * radical 30 = 15 π + 30 π = 45 π