Marek paints a cylinder to paint 8 square feet he uses 1 quart of paint. The height of the cylinder is 4 feet and the radius is 0.5 feet if he doesn't paint the top of cylinder how much lint will he need?

Respuesta :

Answer:

  1.67 quarts

Step-by-step explanation:

For a cylinder of radius r and height h, the lateral area is ...

  LA = 2πrh

The area of one end is ...

  A = πr²

Then the total surface area of the side of the cylinder and one end is ...

  S = LA +A = πr(2h+r)

For the given dimensions, the area to be painted is ...

  S = π(0.5)(2·4 +0.5) = 4.25π ≈ 13.352 . . . . square feet

If one quart paints 8 ft², then the number of quarts of paint needed is ...

  (13.352 ft²)/(8 ft²/qt) = 1.67 qt

Marek will need about 1.67 quarts of paint for his cylinder.