The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. The area of the playground in m² is :
Strengthen your preparation for Class 9th Maths with NCERT solutions and MCQ-based questions from Chapter 11: Surface Areas and Volumes. Practice exercise questions, short-answer problems and clear explanations to master concepts like finding surface areas and volumes of solids and their combinations. These resources are designed as per the CBSE syllabus for thorough exam preparation. Consistent practice will enhance your confidence and problem-solving abilities. Access step-by-step solutions and revision notes crafted for success. Start today to secure higher scores in exams.
Share
Explanation:
The roller is a cylinder, and the area it covers in one complete revolution is equal to its curved surface area (CSA). The formula for the CSA of a cylinder is:
CSA = 2πrh,
where:
– r is the radius of the circular base,
– h is the length (or height) of the cylinder.
From the problem:
– The diameter of the roller is 84 cm, so the radius (r) is:
r = Diameter / 2 = 84 / 2 = 42 cm = 0.42 m (converted to meters),
– The length (h) of the roller is 120 cm = 1.2 m (converted to meters).
Substitute the values of r = 0.42 m and h = 1.2 m into the formula:
CSA = 2πrh.
Using π ≈ 22/7 for calculation:
CSA = 2 × (22/7) × 0.42 × 1.2.
Simplify step by step:
CSA = 2 × (22/7) × 0.504,
CSA = 2 × 22 × 0.072,
CSA = 3.168 m².
This is the area covered by the roller in one complete revolution. Since the roller takes 500 revolutions to level the playground, the total area of the playground is:
Total Area = CSA × Number of Revolutions,
Total Area = 3.168 × 500,
Total Area = 1584 m².
Thus, the area of the playground is 1584 m², which corresponds to option a) 1584.
For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-9/maths/