Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has a diameter of twelve inches and a height of 2 inches. Each leg is 3 inches by 3 inches by fourteen inches. How much area will Evan have to paint? Use three point one four for pi. Show your work.
seat has
top area of pi*6^2 = 36pi
side area of 2*pi*6*2 = 24pi
bottom area of 36pi - 4(3*3) = 36pi - 36
(bottom has 4 legs attached, not painted where fastened)
each leg has area of 4*(3*14) = 168
(don't paint top of leg or bottom of leg)
total area = 36pi + 24pi + 36pi-36 + 168
= 96pi + 132
= 433.44
i also believe that it is 433.44 but i am not sure i will hit u up when i do though
896.4 inch² is what another person says on a website well hop it helps good luck :D
To find the area that Evan will have to paint, we need to calculate the surface area of the cylindrical seat and the four rectangular prism legs.
1. Surface area of the cylindrical seat:
The formula for the surface area of a cylinder is given by: A = 2πrh + πr^2, where r is the radius and h is the height.
Given that the diameter of the seat is 12 inches, the radius would be half of that, which is 12/2 = 6 inches. The height of the seat is given as 2 inches.
Substituting these values into the formula, we get: A = 2 * 3.14 * 6 * 2 + 3.14 * 6^2 = 2 * 3.14 * 12 + 3.14 * 36 = 75.36 + 113.04 = 188.40 square inches.
Therefore, the surface area of the cylindrical seat is 188.40 square inches.
2. Surface area of the rectangular prism legs:
The formula for the surface area of a rectangular prism is given by: A = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively.
Given that each leg has dimensions of 3 inches by 3 inches by 14 inches, we can substitute these values into the formula:
A = 2 * 3 * 3 + 2 * 3 * 14 + 2 * 3 * 14 = 18 + 84 + 84 = 186 square inches.
Therefore, the total surface area of the four rectangular prism legs is 186 square inches.
To find the total area that Evan will have to paint, we add the surface area of the seat and the surface area of the legs:
Total area = Surface area of seat + Surface area of legs
Total area = 188.40 + 186 = 374.40 square inches.
Therefore, Evan will have to paint approximately 374.40 square inches.