MathematicsThe radii of the circular ends of the frustum of a cone of height 45 cm  are 28cm and 7cm. Find its volume and curved surface area.

The radii of the circular ends of the frustum of a cone of height 45 cm  are 28cm and 7cm. Find its volume and curved surface area.


  1. A
    48510 c m 2   , 330 274 c m 2  
  2. B
    58510 c m 2   , 300 274 c m 2  
  3. C
    48510 c m 2   , 300 274 c m 2  
  4. D
    58510 c m 2   , 330 274 c m 2   

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    Solution:

    Given,
    Height of the frustum of a cone = 45cm
    Radii of the frustum of a cone are 28cm and 7cm
    We know that the volume of the frustum of a cone of lower radius, r, upper radius, R, and height, h is given by V= πh 3 R 2 + r 2 +Rr  
    We get,
    V= π 45 3 28 2 + 7 2 + 28 7 V= 22 7 × 45 3 784+49+196 V= 22 7 × 45 3 784+49+196 V= 22 7 ×15×1029 V=48510c m 3  
    Now, the curved surface area of a frustum of cone of upper radius, r, lower radius, R, slant height, l and height, h is given by πl R+r   where l= h 2 + Rr 2  .
    Substituting r = 7, R = 28 and h = 45 in l= h 2 + Rr 2  .
    We get,
      l= 45 2 + 287 2 l= 2025+441 l= 2466 l=3 274 cm   Therefore, the slant height of the frustum of a cone is 3 274   cm.
    We get,
    CSA=πl R+r CSA= 22 7 ×3 274 × 28+7 CSA= 22 7 ×3 274 ×35 CSA=330 274 c m 2  
    Thus, the volume of the frustum of a cone is 48510 c m 2   and the curved area of the frustum of a cone is 330 274 c m 2  .
    Hence, the correct option is 1.
     
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