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Probability

Question
CBSEENMA9003563

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.   

Solution

For heap of wheat
Diameter = 10.5 m
therefore Radius (r) = fraction numerator 10.5 over denominator 2 end fraction space cm space equals space 5.25 space straight m
     Height (h) = 3 m
therefore  Volume = 1 third πr squared straight h
space space space space space space space space space space space space space space space space space space space equals 1 third cross times 22 over 7 cross times left parenthesis 5.25 right parenthesis squared cross times 3
space space space space space space space space space space space space space space space space space space space space equals space 86.625 space straight m cubed
Slant space height space left parenthesis straight l right parenthesis space equals space square root of straight r squared plus straight h squared end root
space space space space space space space space space space space space space space space space equals square root of left parenthesis 5.25 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root
space space space space space space space space space space space space space space space space equals space square root of 27.5625 plus 9 end root
space space space space space space space space space space space space space space space space space equals square root of 36.5625 end root equals 6.05 space straight m left parenthesis approx. right parenthesis
therefore   Curved surface area = πrl
       equals 22 over 7 cross times 5.25 cross times 6.05 equals 99.825 space straight m squared
Hence, the area of the canvas required is 99.825 m2. .