25123.5325 square feet of tin is needed to make the roof
Solution:
Given that the roof of a farm silo is the shape of a hemisphere and is made of sheet tin
Given diameter of silo = 126.5 feet
[tex]Radius = \frac{diameter}{2}[/tex]
[tex]r = \frac{126.5}{2} = 63.25[/tex]
To find: sheet tin is needed to make the roof
So we have to find the curved surface area of hemisphere
The curved surface area of hemisphere is given as:
[tex]\text{ curved surface area } = 2 \pi r^2[/tex]
Substitute r = 63.25 in above formula
[tex]\text{ curved surface area } = 2 \times 3.14 \times (63.25)^2\\\\\text{ curved surface area } = 6.28 \times 4000.5625\\\\\text{ curved surface area } = 25123.5325[/tex]
Thus 25123.5325 square feet of tin is needed to make the roof
