Volume and Surface Area of Solid Figures


  1. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per sq m is ₹15000, then find the height of the hall ?









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    Area of 4 wails = Lateral surface area perimeter = 2(l + b) = 250
    ⇒ l + b = 250/2 = 125 m
    Area to be painted = Cost/Rate = 15000/10 = 1500 sq m
    Area of 4 wails = 2(l + b)h = 250 h

    Correct Option: B

    Area of 4 wails = Lateral surface area perimeter = 2(l + b) = 250
    ⇒ l + b = 250/2 = 125 m
    Area to be painted = Cost/Rate = 15000/10 = 1500 sq m
    Area of 4 wails = 2(l + b)h = 250 h
    ⇒ 250h = 1500
    ∴ h = 1500/250 = 6 m


  1. The diameter of a roller is 84 cm and its length 120 cm. Its takes 500 complete revolutions to move once over to level a playground (in sq m) ?









  1. View Hint View Answer Discuss in Forum

    In one revolution, area covered = Covered surface area
    ⇒ 2πrh = 2 x (22/7) x 42 x 120 = 31680 sq cm
    in 500 revolutions,
    Area covered = 31680 x 500

    Correct Option: D

    In one revolution, area covered = Covered surface area
    ⇒ 2πrh = 2 x (22/7) x 42 x 120 = 31680 sq cm
    in 500 revolutions,
    Area covered = 31680 x 500 = (1584 x 104) sq cm
    = (1584 x 104) / (104) = 1584 sq m



  1. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the covered surface of the pillar at the rate ₹ 10 per sq m . ?









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    Curved surface area = 2πrh
    = 2 x (22/7) x 0.25 x 3.5

    Correct Option: D

    Curved surface area = 2πrh
    = 2 x (22/7) x 0.25 x 3.5
    = 5.5 sq m
    ∴ Cost of painting 5.5 sq m = 10 x 5.5
    = ₹ 55


  1. A pillar 14 cm in diameters is 5 m high. How much material was used to construct it ?









  1. View Hint View Answer Discuss in Forum

    Volume of the cylinder = πr2h

    Correct Option: D

    Volume of the cylinder = πr2h
    = (22/7) x 7 x 7 x 500 = 77000
    = (77 x 103) cm3



  1. The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. what is the slant height of the cone ?









  1. View Hint View Answer Discuss in Forum

    Curved surface area of right circular cone = πrl
    ∴ 440 = (22/7) x 14 x l

    Correct Option: A

    Curved surface area of right circular cone = πrl
    ∴ 440 = (22/7) x 14 x l
    ⇒ l = (440 x 7) / (22 x 14) = 10 cm