Question

What is the maximum number of cylindrical pencils of 0.5 cm diameter that can be stood in a square shaped stand of 5 cm ď‚´ 5 cm inner cross section?

Answer 1

The edge of the square stand = 5 cm
The diameter of each pencil = 0.5 cm
So, this means that 1 pencil needs 0.5 cm of length of the stand
And we have the total length as 5 cm
So, in 5 cm edge length, no. of pencils that can be kept across will be =
5 cm / 0.5 cm = 10
So, 10 pencils can be kept in 1 line across.

Similarly, 10 pencils can be kept downwards in the square stand

So, total no. of pencils that can be kept in the stand will be
10 x 10 = 100
Therefore, 100 pencils max can be kept in the stand.

Answer 2

Along an edge of the square, the length of the square's side should equal the sum of diameter of all pencils lying along the edge.
The diameter of one pencil is 0.5 cm. Total length of side of square is 5 cm. So, total number of pencils lying along the edge is 5/0.5 = 10 pencils.
Total number of pencils is 10×10 = 100 pencils.

So, 100 pencils can be kept in the square pencil stand.