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  1. Asked: In:

    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. Find the area of the playground in m².

    rajesh joshi

    Radius of roller r = 84/2 = 42 cm = 0.42 m and length h = 120 cm = 1.2 m outer curved surface area of roller = 2πrh = 2 × 22/7 × 0.42 × 1.2 = 2 × 22 × 0.06 × 1.2 = 3.168 m² Area of ground levelled in on revolution = 3.168 m² Therefore, area of ground levelled in 500 revolutions = 500 × 3.168 = 1584Read more

    Radius of roller r = 84/2 = 42 cm = 0.42 m and length h = 120 cm = 1.2 m
    outer curved surface area of roller = 2πrh
    = 2 × 22/7 × 0.42 × 1.2 = 2 × 22 × 0.06 × 1.2 = 3.168 m²
    Area of ground levelled in on revolution = 3.168 m²
    Therefore, area of ground levelled in 500 revolutions = 500 × 3.168 = 1584 m²
    Hence, the area of playground is 1584 m².

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  2. Asked: In:

    A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs 12.50 per m².

    rajesh joshi

    Radius of cylindrical pillar r = 50/2 = 25 cm = 0.25 m and height h = 3.5 m Curved surface area of cylindrical pillar = 2πrh = 2 × 22/7 × 0.25 × 3.5 = 2 × 22 × 0.25 × 0.5 = 5.5 m² Cost of painting 1 m² area = Rs. 12.50 Therefore, cost of painting 5.5 m² area = Rs. 12.50 × 5.5 = Rs 68.75 Hence, the tRead more

    Radius of cylindrical pillar r = 50/2 = 25 cm = 0.25 m and height h = 3.5 m
    Curved surface area of cylindrical pillar = 2πrh
    = 2 × 22/7 × 0.25 × 3.5 = 2 × 22 × 0.25 × 0.5 = 5.5 m²
    Cost of painting 1 m² area = Rs. 12.50
    Therefore, cost of painting 5.5 m² area = Rs. 12.50 × 5.5 = Rs 68.75
    Hence, the total cost of painting the cylindrical pillar is Rs 68.75.

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  3. Asked: In:

    Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height.

    rajesh joshi

    Curved surface area of cylinder 4.4 m² and radius r = 0.7 m Let, the height of cylinder = h m Curved surface area of cylinder = 2πrh ⇒ 4.4 = 2 × 22/7 × 0.7 × h ⇒ 4.4 = 4.4h ⇒ h = 1 m Hence, the height of the cylinder is 1 m.

    Curved surface area of cylinder 4.4 m² and radius r = 0.7 m
    Let, the height of cylinder = h m
    Curved surface area of cylinder = 2πrh
    ⇒ 4.4 = 2 × 22/7 × 0.7 × h ⇒ 4.4 = 4.4h ⇒ h = 1 m
    Hence, the height of the cylinder is 1 m.

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  4. Asked: In:

    The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.

    rajesh joshi

    Curved surface area of cylinder 88 cm² and height h = 14 cm Let, the radius of base of cylinder = r cm Curved surface area of cylinder = 2πrh ⇒ 88 = 2 × 22/7 × r × 14 ⇒ 88 = 88r ⇒ r = 1 cm Hence, the diameter of base of cylinder = 2r = 2 × 1 = 2 cm.

    Curved surface area of cylinder 88 cm² and height h = 14 cm
    Let, the radius of base of cylinder = r cm
    Curved surface area of cylinder = 2πrh
    ⇒ 88 = 2 × 22/7 × r × 14 ⇒ 88 = 88r ⇒ r = 1 cm
    Hence, the diameter of base of cylinder = 2r = 2 × 1 = 2 cm.

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  6. Asked: In:

    It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?

    rajesh joshi

    Radius of base of cylinder r = 140/ 2 = 70 cm 0.7 m and height h = 1 m Total surface area of cylinder = 2πr(r + h) = 2 × 22/7 × 0.7(0.7 + 1) = 4.4 × 1.7 = 7.48 m² Hence, 7.48 square meter metal sheet is required to make the closed cylindrical tank.

    Radius of base of cylinder r = 140/ 2 = 70 cm 0.7 m and height h = 1 m
    Total surface area of cylinder = 2πr(r + h)
    = 2 × 22/7 × 0.7(0.7 + 1) = 4.4 × 1.7 = 7.48 m²
    Hence, 7.48 square meter metal sheet is required to make the closed cylindrical tank.

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