Evan is painting a stool that has a cylindrical seat and four rectangular prism legs. The seat has a diameter of 8 inches and a height of 2 inches. Each leg is 2 inches by 2 inches by ten inches. How much area will Evan have to paint? Use three point one four for pi. Show your work.

Question

anonymous · Answer

Since paint goes on the surface of the stool, you will need to find the surface area. I don't like these questions because they don't tell you if you have to paint the underside of the seat -- usually that is not painted, and sometimes they get really picky about where the legs are attached to the seat -- do you have to subtract that on both the seat and the ends of the legs? and do you have to paint the ends of the legs that will rub against the floor? Usually that is not painted and a glider foot is nailed on. But if everything gets painted and you need to show your work, here is how: 


The surface area of the cylinder seat ~ 
Top and underside of seat 
2 (one for top and one for bottom) pi radius squared is 
2 x 3.14 x 4² = 100.48 square inches 
edge of seat 
pi x diameter (this gives the circumference - distance around) x height is 
3.14 x 8 x 2 = 50.24 square inches 

You must add 100.48 + 50.24 to get total surface area of the seat 

For the legs 

4 (because there are four legs) x height x perimeter of standing leg is 
4 x 10 x ( 2 + 2 + 2 + 2 ) = 4 x 10 x 8 = 320 square inches for the legs. 
This does not paint the ends of the legs. If you need that, add the area of the ends of each leg. One leg is 2 x 2 = 4. 

Add the seat area to the legs area; this will be your final answer. 

unless... 
If you do not have to paint the underside of the seat, then skip the 2 in the first step.

anonymous · Answer

Thanks! Can you help me with a few more?

anonymous · Answer

Describe two methods to solve for the volume of the composite shape shown.