Answer:
[tex]\approx[/tex] 57 gallons
Step-by-step explanation:
Given:
Silo needs to be painted.
Height of silo = 80 feet
Diameter of silo = 20 feet
One gallon of paint covers 100 sq ft
To find:
Gallons of Paint required to paint the outside of silo = ?
Solution:
We need to first calculate the lateral surface area(LSA) of this cylinder shaped silo.
[tex]LSA = 2\pi rh[/tex]
where r is the radius and
h is the height of cylinder.
[tex]r = \dfrac{Diameter}2\\\Rightarrow r = 10\ ft[/tex]
Putting the values in formula:
[tex]LSA = 2\times 3.14\times 10\times 80\\\Rightarrow LSA = 5024\ sq \ ft[/tex]
Total surface area of cylinder = LSA + 2 [tex]\times[/tex] Area of base
Total surface area of cylinder = LSA + 2 [tex]\times[/tex] [tex]\pi r^{2}[/tex]
TSA = [tex]5024 +2 \times 3.14 \times 10^2 = 5024 +628=5652\ sq \ ft[/tex]
100 sq ft requires number of gallons = 1
5652 sq ft requires number of gallons:
[tex]\dfrac{1}{100} \times 5652 \approx 57\ gallons[/tex]
