The semi-vertical angle of a cone is 45°. If the height of the cone is 20.025, then its approximate lateral surface area, is

The semi-vertical angle of a cone is 45°. If the height of the cone is 20.025, then its approximate lateral surface area, is

  1. A

    4012π

  2. B

    4002π

  3. C

    3992π

  4. D

    none of these

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Let r be the radius, h be the height and I be the slant

    height of a cone of semi-vertical angle 45°. Then,

    r=h and I=2h

    Let h=20 and h+Δh=20.025Δh=0.025

    Let S be the lateral surface. Then,

    S=2πh2                                             [S=πrlS=πh×2h]dSdh=22πh dSdhh=20=402π ΔS=dSdhΔhΔS=402π×0.025=2π

    Also, at h=20, we have S=4002π

     S+ΔS=4002π+2π=4012π

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.