Question

The exterior surface of a farm silo needs to be painted. If one gallon of paint covers 224 square feet, what is the minimum number of gallons needed to paint the silo? Keep in mind that the bottom of the silo is not painted. Use π=3.14.

a. 10 gallons
b. 15 gallons
c. 20 gallons
d. 25 gallons

Answer 1

To find the minimum number of gallons needed to paint the silo, calculate the total surface area of the silo and divide it by the coverage rate of one gallon of paint. The radius and height of the silo are needed to calculate the surface area. Use the formula: Number of gallons = (πr^2 + 2πrh) / 224.

Step-by-step explanation:

The area of a circle is given by the formula A = πr^2, where r is the radius. The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height.

Since only the exterior surface needs to be painted, we don't include the bottom circle. So the total surface area of the silo is A = πr^2 + 2πrh. Now, let's substitute the values into the formula:

1. Calculate the area of the top circle: A_top = πr^2.
2. Calculate the area of the lateral surface: A_lateral = 2πrh.
3. Add the areas together: A_total = A_top + A_lateral = πr^2 + 2πrh.
4. Divide the total surface area by the coverage rate of one gallon of paint: Number of gallons = A_total / 224.
5. Simplify the expression and calculate the minimum number of gallons:

Number of gallons = (πr^2 + 2πrh) / 224.

Finally, substitute the given values of r and h into the formula to find the minimum number of gallons needed to paint the silo.