Question

the roof of a farm silo is the shape of a hemisphere and is made of sheet tin. if the diameter of the silo is 126.5 feet, how much sheet tin is needed to make the roof?

Answer 1

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

$Radius = \frac{diameter}{2}$

$r = \frac{126.5}{2} = 63.25$

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:

$\text{ curved surface area } = 2 \pi r^2$

Substitute r = 63.25 in above formula

$\text{ curved surface area } = 2 \times 3.14 \times (63.25)^2\\\\\text{ curved surface area } = 6.28 \times 4000.5625\\\\\text{ curved surface area } = 25123.5325$

Thus 25123.5325 square feet of tin is needed to make the roof