## Task 2 - 010512

In the workshop, stands for 5 test tubes each are to be manufactured. The upper board is $160 \mathrm{~mm}$ long.

It is to have 5 drill holes, each with a diameter of $18 \mathrm{~mm}$. The distance from the center of the first and last hole to the ends of the board is $24 \mathrm{~mm}$ each. All drill holes should be equally spaced.

a) What is the distance from the center of one hole to the center of the next?

b) What are the spaces between the edges of the drill holes?
For the given quantities (see figure): length of the board $l=160 \mathrm{~mm}$, diameter of a hole $d=18 \mathrm{~mm}$, and the distance between the edge bores and the edge $r=24 \mathrm{~mm}$. The distances between the centers of two holes $a$ and the distance between two bores $b$ are to be determined.

a) Since the distance $r$ occurs on both the left and right sides, the remaining length for the four distances between the bores is $l-2 r$, and thus $a=\frac{1}{4}(l-2 r)=28 \mathrm{~mm}$.

The distance from the center of one hole to the center of another hole is $28 \mathrm{~mm}$.

b) Since a bore has a radius of $\frac{d}{2}$, it follows that $b=a-2 \frac{1}{2} d=10 \mathrm{~mm}$. The space between two bores is $10 \mathrm{~mm}$.