Question

An auditorium has 20 large cylindrical columns. Each column has a height of 22 feet from the floor to the ceiling and a diameter of 2.5 feet. How many gallons of paint, to the nearest whole number, must be purchased to paint the lateral surface area of the columns if each gallon of paint covers 350 square feet?

Answer 1

10 Gallons

Explanation:

Height of each of the Column=22 feet

Diameter of each of the column=2.5 feet

Therefore:Radius of each of the column=2.5÷2=1.25 Feet

Lateral Surface Area of a Cylinder=2πrh

Lateral Surface Area of one column=2*π*1.25*22

=55π square feet

Since there are 20 columns,

Total Lateral Surface Area of all the columns=20*55π

=1100π Square Feet.

1 gallon will paint 350 square feet

Therefore:

Number of gallons that will paint 1100π square feet=1000π÷350

=9.87 ≈10 gallons (to the nearest whole number)