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ICSE Class 10 Answered

A bucket made of a metal sheet is in the form of a cone whose height is 35 cm and diameter of circular ends are 30cm and 12cm.How many litres of milk will it contain if it is filled upto the brim.  
Asked by rajmumbai1973 | 05 Jan, 2019, 06:52: PM
answered-by-expert Expert Answer
As given in question,  bucket's lateral cross section ABCD is shown in figure with dimensions in cm.
As can be seen that, volume of bucket is part of the volume of full cone.
To get the volume of full cone we need to find the height EG using the similar triangles Δ EFB and Δ EGC.
 
begin mathsize 12px style fraction numerator E F over denominator E G end fraction space equals space fraction numerator h over denominator h plus 35 end fraction space equals space fraction numerator F B over denominator E C end fraction space equals space 6 over 15 end style
we get h = (70/3) cm
 
volume of the bucket = begin mathsize 12px style 1 third pi cross times 15 cross times 15 cross times left parenthesis 70 over 3 plus 35 right parenthesis space space minus space 1 third cross times pi cross times 6 cross times 6 cross times 70 over 3 space almost equal to space 12865 space c m cubed end style  = 12.865 Litre
Answered by Thiyagarajan K | 06 Jan, 2019, 07:49: PM

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