MathematicsA bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8   cm 3  . The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. (Use π=3.14)  

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8   cm 3  . The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. (Use π=3.14)  


  1. A
    15cm
  2. B
    20cm
  3. C
    25cm
  4. D
    21cm 

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    Solution:

    Given,
    Capacity of the bucket = 12308.8   cm 3  
    Upper radius of the bucket = 20cm
    Lower radius of the bucket = 12cm
    We know that the volume of a frustum of a cone having radii, r and R, and height, h is given by πh 3 R 2 + r 2 +Rr  .
    We get,
    12308.8= πh 3 20 2 + 12 2 + 20 12   12308.8= 3.14×h 3 400+144+240  
    12308.8= 3.14×h 3 784  
    h= 12308.8×3 3.14×784 h=15cm  
    Therefore, the height of the bucket is 15 cm.
    Hence, the correct option is 1.
     
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