Bunuel wrote:
The largest possible cube is enclosed in a cylinder and has volume x. What is the volume of the cylinder?
(1) x is 27.
(2) The height of the cylinder is 5 units.
Refer the top view in the enclosed diagram(When a cube is inserted in a cylinder)
Given, volume of cube=x.
So, length of sides of the cube = \(\sqrt[3]{x}\)
Diagonal of cross-section or Top/Bottom surface(Which is a circle) of the cylinder=Diagonal of cube(Top view is a square-one face of cube)=\(\sqrt{2}*\sqrt[3]{x}\)
or 2* radius=\(\sqrt{2}*\sqrt[3]{x}\)
Or \(r=\frac{\sqrt[3]{x}}{\sqrt{2}}\)
Question stem:- What is the volume of the cylinder?
Vol. of cylinder=\(\pi*r^2*h\)
We need the value of h.
St1:-
x=27So, \(r=\frac{\sqrt[3]{27}}{\sqrt{2}}\)=\(\frac{3}{\sqrt{2}}\)
height is not known or variable. Area of cylinder is not unique.
Insufficient.
St2:- The height of the cylinder is 5 units. Or, h=5 unit
The largest possible length of sides of the cube can be 5 unit . If length of sides of the is greater than 5 unit then it can't be enclosed fully inside the cylinder with h=5 unit.
So, diagonal of circle, 2r=\(5\sqrt{2}\)
Hence, volume of cylinder can be calculated. (radius and height are known)
Sufficient.
Ans. (B)
Attachments
cyl.JPG [ 23.47 KiB | Viewed 997 times ]
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Regards,
PKN
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