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.

Question

jack1 · Answer

assuming that the 2 inches of the chair legs are within the seat as the means of joining...?
or is he painting the entirety and joining the wood legs externally flush against the seat?

jack1 · Answer

@jenflo0810 ...? which is ur assumption?

anonymous · Answer

the first one

jack1 · Answer

ok so first we'll analyse the surface area of the seat part
seat is a cylinder
diameter 12 inchs
height 2 inches
surface area = ?

jack1 · Answer

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jack1 · Answer

@jenflo0810 what's the area of the top and bottom part of it?

anonymous · Answer

First, let's find the surface area of one rectangular prism. (take into account that the top part won't be painted as it is attached to the cylindrical seat.)

2(3*14+3*14)+3*3
2(42+42)+9
2(84)+9
168+9
177

The surface area that needs to be painted for the four legs:

4(177)
708inch^2

The surface area of the seat:
(keep in mind that the diameter is 12 and to find its radius, you need to divide the diameter in half. r=6)

2(3.14*6*6)+2*3.14*6*2
226.08+75.36
301.44inch^2

Now, minus the area that is covered by the top of the legs.

4(3*3)
36inch^2

301.44-36
=265.44inch^2

Add the the surface areas that you want to paint, to find the total surface area that evan has to paint.

708+265.44
=973.44inch^2

jack1 · Answer

...or u could do it all for her...
;D

anonymous · Answer

im sorry D: 
i did it step by step though :l