Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Surface Areas and Volumes

Previous Year Questions (2022-2024)

📅 Year 2022

  1. A cone of radius 3 cm and height 4 cm is filled with water. Water is poured into cylinder of radius 3 cm. Find water height in cylinder.
    Show Solution
    Volume of cone = 13πr2h = 13π(32)(4) = 12π cm3\nVolume of cylinder = πr2h = π(9)h = 9πh\n9πh = 12π => h = 43 cm
  2. A sphere of radius 6 cm is melted and recast into cones of radius 2 cm and height 6 cm. Find number of cones.
    Show Solution
    Volume of sphere = 43π(63) = 288π cm3\nVolume of one cone = 13π(22)(6) = 8π cm3\nNumber = 288π8π = 36

📅 Year 2023

  1. A cone of radius 3 cm and height 4 cm is filled with water. Water is poured into cylinder of radius 3 cm. Find water height in cylinder.
    Show Solution
    Volume of cone = 13πr2h = 13π(32)(4) = 12π cm3\nVolume of cylinder = πr2h = π(9)h = 9πh\n9πh = 12π => h = 43 cm
  2. A sphere of radius 6 cm is melted and recast into cones of radius 2 cm and height 6 cm. Find number of cones.
    Show Solution
    Volume of sphere = 43π(63) = 288π cm3\nVolume of one cone = 13π(22)(6) = 8π cm3\nNumber = 288π8π = 36

📅 Year 2024

  1. A cone of radius 3 cm and height 4 cm is filled with water. Water is poured into cylinder of radius 3 cm. Find water height in cylinder.
    Show Solution
    Volume of cone = 13πr2h = 13π(32)(4) = 12π cm3\nVolume of cylinder = πr2h = π(9)h = 9πh\n9πh = 12π => h = 43 cm
  2. A sphere of radius 6 cm is melted and recast into cones of radius 2 cm and height 6 cm. Find number of cones.
    Show Solution
    Volume of sphere = 43π(63) = 288π cm3\nVolume of one cone = 13π(22)(6) = 8π cm3\nNumber = 288π8π = 36