Mensuration

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Aptitude miscellaneous
  1. The perimeter of the floor of a room is 18 m. What is the area of the walls of the room, if the height of the room is 3 m ?








  1. View Hint View Answer Discuss in Forum

    Area of four walls of a room = 2(length + breadth) × height
    = Perimeter of floor × height = 18 × 3 = 54 m²

    Correct Option: C

    Area of four walls of a room = 2(length + breadth) × height
    = Perimeter of floor × height = 18 × 3 = 54 m²

  1. The length (in metres) of the longest rod that can be put in a room of dimensions 10 m × 10 m × 5 m is








  1. View Hint View Answer Discuss in Forum

    Length of the longest rod Diagonal = √10² + 10² + 5² = √225 = 15 metre

    Correct Option: B

    Length of the longest rod Diagonal = √10² + 10² + 5² = √225 = 15 metre

  1. The floor of a room is of size 4 m × 3 m and its height is 3 m. The walls and ceiling of the room require painting. The area to be painted is








  1. View Hint View Answer Discuss in Forum

    Area of the four walls of the room = 2 × height (length × breadth)
    = 2 × 3 (4 + 3) = 42 sq. metre
    Area of ceiling = 4 × 3 = 12 sq. metre
    ∴ Total area = 42 + 12 = 54 sq. metre

    Correct Option: B

    Area of the four walls of the room = 2 × height (length × breadth)
    = 2 × 3 (4 + 3) = 42 sq. metre
    Area of ceiling = 4 × 3 = 12 sq. metre
    ∴ Total area = 42 + 12 = 54 sq. metre

  1. If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm² respectively, then the maximum length of a stick that can be placed inside the box is








  1. View Hint View Answer Discuss in Forum

    Let the length, breadth and height of the box be x, y and z cm respectively.
    ∴ x + y + z = 12 ...(i)
    and 2 (xy + yz + zx) = 94 ...(ii)
    ∴ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
    ⇒ 144 = x² + y² + z² + 94
    → x² + y² + z² = 144 – 94 = 50
    ∴ Maximum length of stick = √x² + y² + z²
    = √50 = 5√2cm

    Correct Option: A

    Let the length, breadth and height of the box be x, y and z cm respectively.
    ∴ x + y + z = 12 ...(i)
    and 2 (xy + yz + zx) = 94 ...(ii)
    ∴ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
    ⇒ 144 = x² + y² + z² + 94
    → x² + y² + z² = 144 – 94 = 50
    ∴ Maximum length of stick = √x² + y² + z²
    = √50 = 5√2cm

  1. If the length of the diagonal of a cube is 8√3cm, then its surface area is








  1. View Hint View Answer Discuss in Forum

    If the length of the edge of cube be x cm, then
    diagonal = √3x cm
    ∴ √3x = 8√3 ⇒ x = 8cm
    ∴ Surface area of the cube = 6x² = 6 × 8 × 8 = 384 sq. cm

    Correct Option: D

    If the length of the edge of cube be x cm, then
    diagonal = √3x cm
    ∴ √3x = 8√3 ⇒ x = 8cm
    ∴ Surface area of the cube = 6x² = 6 × 8 × 8 = 384 sq. cm