Question

A man carves out a cylinder of the largest possible volume from a cubical block of wood if the wooden block has a side of 15 cm fe volume of the remaining wood.
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Answer 1

Answer:

[(64 x 8 x  5root5) / 625 x 25] m^3

Step-by-step explanation

Answer 2

Given,

A wooden block of side 15 cm.

To find,

Cylinder with maximum volume that can be carved out from the cubical block.

Solution,

To carve the cylinder with the maximum volume, we will take a cylinder whose diameter will be equal to the length of the side of the cubical box.

The diameter of the cylinder will be 15 cm.

Radius of the cylinder = 7.5cm

The volume of the cylinder is given by $\pi r^{2}h$.

Where r is the radius and h is the height of the cylinder.

Volume  $= \pi ( 7.5 )^{2} *15cm^{3} = 2651.78cm^{3}$

Volume of cube = $s^{3}$ =  $15^{3}cm^{3} = 3375cm^{3}$

We are asked to calculate the remaining volume,

Remaining volume = volume of cube - volume of cylinder.

                                   $= 3375 - 2651.78 cm^{3}\\= 723.2 cm^{3}$

Therefore, $723.2 cm^{3}$ is the remaining volume.