A transmitter tower

A transmitter tower is 80 metres high and is secured to the ground by 4 steel cables, each anchored 60 metres from the base of the tower.
Calculate how many metres of steel cable were needed in total to secure the transmitter tower.
The steel cable has a circular cross-section with a radius of 2 cm. Calculate how much steel was used to produce 1 km of cable. Express the result in m³ and round to 2 decimal places.

Final Answer:

x =  400 m
V =  1.26 m³

Step-by-step explanation:

$$\begin{gathered} n=4 \\ a=80\text{m} \\ b=60\text{m} \\ {x}_1=\sqrt{a^2+b^2}=\sqrt{80^2+60^2}=100\text{m} \\ x=n\cdot x_1=4\cdot 100=400\text{m} \end{gathered}$$

$$\begin{gathered} r=2\text{cm}\to \text{m}=2:100\text{m}=0.02\text{m} \\ l=1\text{km}\to \text{m}=1\cdot 1000\text{m}=1000\text{m} \\ V=\pi \cdot r^2\cdot l=3.1416\cdot 0.02^2\cdot 1000=1.26{\text{m}}^3 \end{gathered}$$

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