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Question about Volume: Cones and Spheres

Math

Originais Teachy

Volume: Cones and Spheres

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(Originais Teachy 2023) - Question Medium of Math

The mayor of a small city plans to build a new square in the shape of a hemisphere, which will serve as a large bird aviary. The aviary will be covered by a metal mesh, and the mayor needs to know the amount of material needed for this cover. Knowing that the radius of the hemisphere is 10 meters, what will be the total area of the metal mesh needed to completely cover the aviary? In addition, the mayor would like to install a water reservoir in the shape of a right cylinder inside the aviary for the birds. The reservoir will have a radius of 2 meters and a height of 5 meters. What will be the volume of water, in cubic meters, that this reservoir can hold?
a.
The area of the metal mesh needed is 300π m² and the volume of water that the reservoir can hold is 30π m³.
b.
The area of the metal mesh needed is 100π m² and the volume of water that the reservoir can hold is 10π m³.
c.
The area of the metal mesh needed is 200π m² and the volume of water that the reservoir can hold is 20π m³.
d.
The area of the metal mesh needed is 400π m² and the volume of water that the reservoir can hold is 40π m³.
e.
The area of the metal mesh needed is 500π m² and the volume of water that the reservoir can hold is 50π m³.

Answer:

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