MathematicsConsider two circular cylinders whose heights are in the ratio 1: 2. The two cylinders have equal volume. What will be the ratio of their radii?

Consider two circular cylinders whose heights are in the ratio 1: 2. The two cylinders have equal volume. What will be the ratio of their radii?


  1. A
    1:√2
  2. B
    √2:1
  3. C
    1:2
  4. D
    1:4 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    It is given that the volume of two circular cylinders is equal and heights are in the ratio 1:2. Consider the heights of the cylinder be h and 2h.
    Let the radii be r 1  and  r 2  .
    We know that,
    The volume of a cylinder is , where r is the radius of the base of the cylinder and h is the height of the cylinder.
    The ratio of their radii will be:
    π r 1 2 h=π r 2 2 2h π r 1 2 h=2π r 2 2 h r 1 2 =2 r 2 2 r 1 2 r 2 2 = 2 1   Taking square root on both sides, we get:
    r 1 r 2 = 2 1 r 1 : r 2 = 2 :1  
    The ratio of the radii is √2:1.
    Therefore, the correct option is 2.
    Chat on WhatsApp Call Infinity Learn