Question

A farmer uses a storage container shaped like a right cylinder to store his corn. The container has a radius of 5 feet and a height of 20 feet. The farmer plans to paint only the side of the cylinder with red paint. If one gallon covers 325 square feet, how many gallons of paint will he need to buy to complete the job?

Answer 1

Answer: To find the area of the side of the cylinder that needs to be painted, we need to calculate the lateral surface area.

The formula for the lateral surface area of a right cylinder is:

Lateral Surface Area = 2πrh

where r is the radius and h is the height of the cylinder.

Plugging in the values:

• r = 5 feet
• h = 20 feet

Lateral Surface Area = 2π(5 feet)(20 feet)

Now we can calculate the lateral surface area:

Lateral Surface Area = 2π(5 feet)(20 feet)

• = 2π(100 square feet)
• = 200π square feet

Since we know that one gallon of paint covers 325 square feet, we can calculate the number of gallons needed:

Number of gallons = Lateral Surface Area / Coverage per gallon

• = (200π square feet) / (325 square feet/gallon)
• = (200π square feet) / (325 square feet/gallon)
• ≈ (200 * 3.14 square feet) / (325 square feet/gallon)
• ≈ 628 square feet / (325 square feet/gallon)
• ≈ 1.932 gallons

Therefore, the farmer will need to buy approximately 1.932 gallons of paint to complete the job.