The cylinder walls of an open-top silo havean outside diamter of 5.0m, thickness of 50cm, and a height of 10m.A can of paint covers 12m^2, and costs 14.98. How much will it cost to paint the silo, including the inside. the outside, and the top of the walls.ANSWER: 374.50 (i don't know how to get it though)
You need to find the three areas. 1- area of outside cylinder = 2 x pi x radius x height 2- area of top. Two calculations required, and you subtract them. Area of a circle is pi x [radius squared] so you first work it out using the 5.0m diameter (1), then work it out using diameter as 5.0m - 10cm (2). The total surface area will be (1) - (2). 3- using the diameter/radius from (2) you can now work out the inside surface area using 2 x pi x radius x height So this gives you the total surface area, divide this by 12m^2 tells you how many cans you need and then multiply by $14.98.
The formula for the surface area of a cylinder is: ?????????? ?????????? ? A = 2??π??r??h You need to paint the inside, the outside, and the top. ———————————————————————————— ? ??????? Let ?r? ?= ?radius of the outer wall ?= ??(5.0m) ?=? 2.5m ? ?????? Wall Thickness ?=? 50cm ?????????? ?????????? ?????????? ? =? 50cm?(1m/100cm) ?????????? ?????????? ?????????? ? = (50/100)m ?????????? ?????????? ?????????? ? = 0.5m ? ????? ????? r? = ?radius of the inside wall = ?r? ? (wall thickness) ?????????? ?????????? ?????????? ?????????? ?????????? ?= r? ? 50cm(1m/100cm) ?????????? ?????????? ?????????? ?????????? ?????????? ?= ?2.5m ? 0.5m ?????????? ?????????? ?????????? ?????????? ???????????? = ?2m ———————————————————————————————————— Then, the total surface to be painted is given by: A ?= ??inside ?+ ?outside ?+ ?[ ?? ???top ?? ??] A ?= ?2??π??r???h ?+ ?2??π??r???h ?+ ?[π??r?? ?? ?π??r??] ?????????? ← now, simplify A ?= ?2??π????h(r? ?+ ?r???) ?+ ?π??[r???? ??r??] ?????????? ???? ← now, substitute for r?, r?, h A ?= ?2??π·10(2 ?+ ?2?.5?) ?+ ?π??[2.5??? ??2?] A ?= ?20??π(4.5?) ?+ ?π??[6.25?? ??4] A ?= ?90??π ?+ ?2.25??π?? A ?= ?92.25??π A ?≈ ?289.812??m? So, the number of cans of paint needed is: Cans ?= ?289.812??m???/??12??m? ?= ?24.151 ?????????? ← We need a little more than ?????????? ?????????? ?????????? ?????????? ?????????? ?????????? ????? 24 cans of paint so that 25 ?????????? ?????????? ?????????? ?????????? ?????????? ?????????? ????? cans must be bought. ?????????? ?????????? ?????????? ?????????? ?????????? ?????????? ??? 25 cans @ $14.98 = $374.50 ?????????? ?????????? ?????????? ?????????? ?????????? ?????????? ????? ?????????? ?????????? ???? ANSWER ————————————————————————————————————
