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 500 times ]

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Regards,

PKN

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