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Home Aptitude Volume and Surface Area See What Others Are Saying!
  • Question
  • If the height, curved surface area and the volume of a cone are h, c and V respectively, then 3?Vh 3 - c 2 + 9V 2 will be equal to?


  • Options
  • A. 0
  • B. 1
  • C. chV
  • D. V2h

  • Correct Answer


  • Explanation

    Let h be the height,
    Volume of the cone = V
    and curved surface area of the cone = c
    ? 1/3 ?r2h = V, ?rl = c
    i.e., ?r?r2 + h2 = c
    ?2r2(r2 + h2) = c2
    Consider 3?Vh3 - c2h2 + 9V2
    = 3? x 1/3?r2h x h3 - ?2r2(r2 + h2)h + 9 x 1/9 x ?2r4 h2
    = ?2r2h4 - ?2r4h2 - ?2r2h4 + ?2r4 = 0


  • More questions

    • 1. 
      ?. x 4 ? 227 = 398
      ?. y 2 + 321 = 346

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

    • Options
    • A. Sunday
    • B. Saturday
    • C. Tuesday
    • D. Wednesday
    • Discuss
    • 3. 1, 4, 9, 16, 23, 25, 36

    • Options
    • A. 9
    • B. 23
    • C. 25
    • D. 36
    • Discuss
    • 4. 
      A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?

    • Options
    • A. ? 2500
    • B. ? 2000
    • C. ? 1500
    • D. Couldn't be determined
    • Discuss
    • 5. 
      If a : b = b : c, then ratio a 4 : b 4 is equal to

    • Options
    • A. ac : b2
    • B. a2 : c2
    • C. c2 : a2
    • D. b2 : ac
    • Discuss
    • 6. 
      A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.

    • Options
    • A. 3 km/h
    • B. 4 km/h
    • C. 4.5 km/h
    • D. 9 km/h
    • Discuss
    • 7. 
      A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?

    • Options
    • A. 2 h
    • B. 21/2 h
    • C. 51/2 h
    • D. 4 h
    • Discuss
    • 8. 
      Find the least number by which 175760 be devided to make it a perfect cube.

    • Options
    • A. 10
    • B. 20
    • C. 100
    • D. 5
    • Discuss
    • 9. 
      The roots of the equation x2 + px + q = 0 are equal if :

    • Options
    • A. p2 = 2q
    • B. p2 = 4q
    • C. p2 = - 4q
    • D. p2 = - 2q
    • Discuss
    • 10. 
      Two cubes have volumes in the ratio 1: 27, The ratio of their surface areas is?

    • Options
    • A. 1 : 3
    • B. 1 : 8
    • C. 1 : 9
    • D. 1 : 18
    • Discuss


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