Question

the outside of the silo shown below needs to be painted.the silo is 80 feet tall and has 20 foot diameter.of one gallon of paint covers 100 square feet how many gallons of paint will be needed you can ignore the doors and windows

Answer 1

`\approx` 57 gallons

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.

`LSA = 2\pi rh`

where r is the radius and

h is the height of cylinder.

`r = \frac{Diameter}2\\\Rightarrow r = 10\ ft`

Putting the values in formula:

`LSA = 2* 3.14* 10* 80\\\Rightarrow LSA = 5024\ sq \ ft`

Total surface area of cylinder = LSA + 2
`*` Area of base

Total surface area of cylinder = LSA + 2
`*`
`\pi r^(2)`

TSA =
`5024 +2 * 3.14 * 10^2 = 5024 +628=5652\ sq \ ft`

100 sq ft requires number of gallons = 1

5652 sq ft requires number of gallons:

`(1)/(100) * 5652 \approx 57\ gallons`