Question

A room is of dimensions 132m × 80m × 105m. How many small cylinders of radius 14m and height 20m can be placed in the given cuboid? with steps

Answer 1

Answer:

In a room of dimensions 132m×80m×105m, 90 small cylinders can be placed.

Step-by-step explanation:

The question is how many small cylinders of radius 14m and height 20cm can be placed in a room of dimensions 132m×80m×105m.

We have given the dimensions, to conclude that it is the room's length, breadth, and height. From the shared values we can calculate the volume.

Volume,  $v=length\times breadth\times height$

           $v=132\times 80\times 105$

             $=1108800 cm^{3}$

The radius of the cylinder is 14m and the height is 20m. So we have the values to find the volume of the cylinder.

         ∴     $v=\pi r^2h$

                $v=3\cdot14\times14^2\times20=12308\cdot8cm^{3}$

To find, how many cylinders can be placed in the given room, we have to divide the two volumes. That is,

$Number\ ofcylinder=\frac{volume\ ofthe\ room}{volume\ ofcylinder}$

∴                       $=\frac{1108800}{12308} \\\\=90$

  We can neglect the decimal value in 12308.8 because we have asked for the number of cylinders. The answer is we can place 90 small cylinders in the room.