Question

An art museum has 20 large cylindrical columns in its lobby. Each column has a height of 22 feet from
the floor to the ceiling and a diameter of 2.5 feet. If a gallon of paint covers 350 square feet, how
many gallons of paint must be purchased to paint the lateral surface area of all of the columns?

Answer 1

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The amount of paint needed to paint 20 pillars is 9.874 gallons.

What is a cylinder?

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

The curved surface area of a single-cylinder with a diameter of 2.5 feet and a height of 22 feet will be,

Curved surface area = πDh = π × 2.5 × 22 = 172.7875 ft²

The total area of 20 pillar = 20 × 172.7875 ft² = 3,455.75191 ft²

Since a gallon of paint can cover only 350 ft², therefore, the amount of paint that will be needed to paint 3,455.75191 ft² can be written as,

$\text{Amount of paint needed} = \dfrac{3,455.75191\rm\ ft^2}{350\rm\ ft^2} = 9.874\rm\ gallons$

Hence, the amount of paint needed to paint 20 pillars is 9.874 gallons.

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