Latest Elitmus Aptitude Question SOLUTION: What is the maximum volume of Right Circular cone which can be cut from solid cuboid having dimension 12*10*15

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(#M40036197) ELITMUS Numerical Ability question Mensuration Keep an EYE

What is the maximum volume of Right Circular cone which can be cut from solid cuboid having dimension 12*10*15

Asked In Elitmus Sukesh Kumar Singh (10 years ago)

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RAKESH  (10 years ago)

3 cases possible
r= min(12,10)/2 = 5 , h = 15 , V = (1/3)*pi*5^2*15 = 125pi
r= min(12,15)/2 = 6 , h = 10 , V = (1/3)*pi*6^2*10 = 120pi
r= min(10,15)/2 = 5 , h = 12 , V = (1/3)*pi*5^2*12 = 100pi

maximum volume = 125pi

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Abhishek Jha  (10 years ago)

Sorry, I went wrong in calculations.. logic is same anyway..

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Abhishek Jha  (10 years ago)

By calculating the area of the cone one by one for all three bases we could find the greatest among them. Area of a right circular cone = 1/3*pie*r^2*h. Here r^2h has to be the greatest.

Now, inside a rectangle, the maximum radius that a circle can have will be (smaller_side of the rect.)/2.
The three rectangles for the base of the cone could be (12, 10), (10, 15), and (15, 12).
We get r^2h as 5^2*12, 5^2*15, and 6^2*15 => 300, 375, and 540.
Hence we find the greatest r^2h to be 540.
So, the greatest volume a right circular cone can have is 1/3*pie*r^2*h = 270pie.

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Soma Ghosh  (10 years ago)

pls explain why to select radius by taking mean of two sides ...??

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Sakshi kochhar  (10 years ago)

why radius is taken minimum of two when we want volume to be maximum

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abinash singh  (10 years ago)

U cant take maximum of radius as u wont be able to create circular base by taking longer side

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