Question

Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has a diameter of fourteen inches and a height of 4 inches. Each leg is 4 inches by 4 inches by eighteen inches. How much area will Evan have to paint? Use three point one four for pi. Show your work

Answer 1

Area of the top of the stool: A = pi*r^2 A = (3.14)*(7)^2 ... The diameter is 14 in, so the radius is 14/2 = 7 in A = 153.86 square inches ----------------------------------- Lateral surface area of the top of the stool A = 2pi*r*h A = 2*(3.14)*7*4 A = 175.84 square inches ------------------------------------- Surface area of one rectangular prism leg (ignoring the top face) SA = 2*(LW+WH+LH) - LW SA = 2*(4*4+4*18+4*18) - 4*4 SA = 2*(4*4+4*18+4*18) - 4*4 SA = 304 There are 4 of these legs. So the total surface area of the legs is 4*304 = 1216 square inches. -------------------------------------- Now add up the area of the top, the sides of the stool, and the legs of the stool to get 153.86 + 175.84 + 304 = 633.7 So Evan will have to paint 633.7 square inches total.