the diameter of a 120 cm long roller is 84 cm It takes 1000 complete revolutions in moving once over to level a playground what is the area of the playground
Answers
Radius of the roller (r) = 84/ 2 cm = 42 cm Length of the roller (h) = 120 cm Curved surface area of the roller = 2πrh = 2 × 22/ 7 × 42 × 120 cm2 = 44 × 720 cm2 = 31680 cm2 ∴ area covered by the roller in 1 revolution = 31680 cm2 ∴ area covered by the roller in 500 revolutions = 31680 × 500 cm2 = 15840000 cm Hence, area of the playground = 15840000/ 100× 100 m2 = 1584 m2
Explanation:
Radius of the roller = diameter ÷ 2 = 84 ÷ 2 = 42 cm
Length of the roller = 120 cm
Curved Surface Area of the Roller (Cylindrical shape) = begin mathsize 16px style 2 πrh space space equals space 2 space cross times 22 over 7 cross times 42 space cross times space 120 space equals space 31680 space cm squared end style
Therefore the area covered by the roller in one revolution = 31680 cm2
Therefore the area covered by the roller in 1000 revolutions = 31680 × 1000 = 31680000 cm2
Therefore the area of the play ground = 31680000 cm2 = 3168 m2
→ l × b = 3168
→ l × 32 = 3168
→ l = 99 m