Question

The length of the diagonal of a wooden cube is 24cm . The cube is cut into the cylinder of the biggest volume possible. The volume of the cylinder is:

Answer 1

Answer:

Answer

Cylinder′sVolume,radius=7cmH=30Volume=722×7×7×30=4620cm3Volumeofcuboid=14×14×30=5880

Remaining volume of wood

5880−4620=1260cm

Answer 2

Answer:

384$\pi$$\sqrt{3}$ $cm^{3}$

Step-by-step explanation:

The diagonal of a Square is $\sqrt{2}$a

The diagonal of a Cube is $\sqrt{3}$a = 24 cm

So side, a =  $\frac{24}{\sqrt{3}} = 8\sqrt{3}$

For a cylinder to be inside the cube its height and diameter should be the same as the cube's side.

So , Diameter, d = $8\sqrt{3}$

Radius, r =  [tex]4\sqrt{3}\\ [/tex]

Height, h = $8\sqrt{3}$

Volume of the cylinder, V = $\pi r^{2} h$

V = $\pi *(4\sqrt{3}) ^{2} *8\sqrt{3}$

V = 2089.497 $cm^{3}$