A semispherical dome of an observatory of a metallic coat needs to be covered. We have $$500 \ m^2$$ of metallic coat and the radius of the semisphere is $$10 \ m$$.
If the strategy is to begin covering the dome from above: Will it be possible to cover the totallity of the surface? In the event that we could not: what will be the height of the covered spherical dome?
Development:
First, we have to check if those $$500 \ m^2$$ of metal coat are enough to cover the entire dome: $$$A_{dome}=\dfrac{4\pi R^2}{2}=628,32 \ m^2$$$ So, the available metallic surface is not enough to cover the dome.
Now, we have to study the height of the covered part of the dome: $$$A_{dome}=2\pi\cdot R \cdot h$$$ $$$500=2\pi\cdot 10 \cdot h$$$ $$$h_{dome}=7,96 \ m$$$
Solution:
It is not possible to cover the whole semisphere. The covered part of the dome has a height of $$7,96 \ m$$.