Question

(100 points, Need help with this ASAP) I bought a used grain silo. I am going to use it as a groom's room at our venue. I am going to paint the inside of it to brighten it up a little. I need to decide how many cans of paint to buy. The silo is 15' across and 10' tall to the top of the cylindrical part. The top of the silo looks like a funnel. It is also 15' across. It is 4' tall. The ceiling is the funnel top. A can of paint covers approximately 400 sq ft. How many cans of paint will I need to buy?

Answer 1

2 cans of paint

Explanation:

Surface area of an open cylinder =
`2\pi rh`

(where r is the radius and h is the height)

⇒ SA = 2 ×
`\pi` × (15 ÷ 2) × 10 = 150
`\pi` ft²

Surface area of an open cone =
`\pi r√(h^2+r^2)`

(where r is the radius and h is the height)

⇒ SA =
`\pi` × (15 ÷ 2) × √(4² + 7.5²) = 63.75
`\pi` ft²

Total surface area = 150
`\pi` + 63.75
`\pi` = 213.75
`\pi` = 671.52 ft² (nearest hundredth)

If one can of paint covers approx. 400 ft² then 2 cans of paint needed to cover 671.52 ft²