B2. We want to mechanically drill a cylindrical borehole with a diameter of $80 \mathrm{~cm}$ on a plot of land. The first meter of drilling costs 10 euros, and each subsequent meter costs 4 euros more than the previous one.

A. How long is the longest cable that we can place in the borehole after $1.5 \mathrm{~m}$ of drilling?

B. How much does the drilling of the fifth meter of the borehole cost?

C. How much would we pay for a $5 \mathrm{~m}$ deep borehole if we receive a $5 \%$ discount when paying in cash?
B2. The diagonal of the cross-section of a cylinder with a diameter of $0.8 \, \text{m}$ and height $1.5 \, \text{m}$ is calculated using the Pythagorean theorem as $d = \sqrt{0.8^2 + 1.5^2} = 1.7 \, \text{m}$.

The cost of digging the first meter is $10 €$, the second meter $14 €$, the third $18 €$, the fourth $22 €$, and the fifth $26 €$.

For a $5 \, \text{m}$ deep hole, we will pay $10 + 14 + 18 + 22 + 26 = 90 €$, with the applied discount it will be $85.50 €$.

![](https://cdn.mathpix.com/cropped/2024_06_07_2a119673c0ca3587e23fg-11.jpg?height=60&width=1559&top_left_y=1632&top_left_x=297)

B. Digging the fifth meter of the hole costs $26 €$ ........................................... 2 t

C. A $5 \, \text{m}$ deep hole costs $90 €, \ldots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .$.

![](https://cdn.mathpix.com/cropped/2024_06_07_2a119673c0ca3587e23fg-11.jpg?height=51&width=1488&top_left_y=1822&top_left_x=364)