SOLUTION: 10 open cylindrical containers are to be painted on the outside, including the base. Each container has a radius of 30cm and a height of 28cm. Take pi=3. (The surface inside the c

Question 1018210: 10 open cylindrical containers are to be painted on the outside, including the base. Each container has a radius of 30cm and a height of 28cm. Take pi=3. (The surface inside the container is not included). Given that 100g of paint is needed to paint an area of 1 square metre, find the amount of paint required to paint the 10 cylinders. Give your answer in kg (2dps).
Thank you so, so much in advance! I keep getting mixed up and confused when I attempt this question so I'd like the expert explanation from someone who can easily do it.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

what you want to do is make all the measurements consistent so that you don't get botched up in the conversions.

you are given that the radius is 30 centimeters and the height is 28 centimeters.

pi is given as 3.

the lateral surface area of a cylinder is equal to 2 * pi * r * h.

when pi = 3 and r = 30 and h = 28, this becomes 2 * 3 * 30 * 28.

the lateral surface area of a cylinder is therefore equal to 5040 square centimeters.

the designation as square centimeters instead of centimeters is important when you have to do the conversions, as you'll soon see.

the area of one of the bases of a cylinder is equal to pi * r^2.

since pi = 3 and r = 30, then the area of one of the bases of a cylinder is equal to 3 * 30^2 = 3 * 900 = 2700 square centimeters.

the area of one of the cylinders that has to be painted is therefore equal to 5040 + 2700 = 7,740 square centimeters.

since you have to paint ten of those cylinders, then the total surface area to be painted is equal to 77,400 square centimeters.

you are given that 100 grams of paint is required to paint 1 square meter.

here's where the conversions come in if you didn't convert up front, which we didn't.

1 square meter is equal to 1 meter * 1 meter.
1 meter is equal to 100 centimeters.
1 square meter is therefore equal to 100 * 100 = 10,000 square centimeters.

if one square meter is equal to 10,000 square centimeters, then divide both sides of that equation to get 1/10,000 square meters is equal to 1 square centimeter.

you have 77,400 square centimeters.
convert that to square meters by multiplying by 1/10,000 to get 7.74 square meters.

you are given that 100 grams of paint are required to paint 1 square meter.

you therefore need 7.74 * 100 = 774 grams of paint to paint 7.74 square meters of cylinder surface area.

1 kilogram is equal to 1000 grams.
divide both sides of this equation by 1000 to get 1/1000 kilograms is equal to 1 gram.

774 grams is therefore equal to 774 * 1/1000 = 774/1000 kilograms which is equal to .774 kilograms of paint.

you need .774 kilograms of paint to paint the 10 cylinders *****

in the preceding, i didn't convert until the end.

it's sometimes better to do all your conversions up front as i'll show you below.

you know that you will eventually have to convert everything to square meters and kilograms, so do the conversion up front and then the problem should flow fairly easily.

let's see how that works.

you are given that the radius is 30 centimeters.
since 1 centimeter = 1/100 meters, then multiply 30 by 1/100 to get 30/100 = .3 meters.

your radius is .3 meters.

likewise your height is .28 meters because 28/100 = .28.

so you have:
r = .3 meters
h = .28 meters

you are given that 100 grams of paint are required to paint 100 square meters.
since 1 gram is equal to 1/1000 kilograms, then multiply 100 grams by 1/1000 kilograms to get 100/100 = .1 kilograms.

you are therefore given that .1 kilograms of paint is required to paint 100 square meters.

now you're ready to go.

you have:

pi = 3
radius = .3 meters
height = .28 meters
.1 kilograms of paint are required to paint 100 square meters of surface area.

your formulas are the same:
lateral surface area of one cylinder is equal to 2 * pi * r * h.
area of the base of the cylinder is equal to pi * r^2.

lateral surface area of one cylinder becomes 2 * 3 * .3 * .28 = .504 square meters.

area of the base of one of cylinder is equal to 3 * .3^2 = .27 square meters.

add them up and the surfaces area of one cylinder to be painted is .774 square meters.

you have 10 cylinders to be painted, so the total surface area to be painted is 7.74 square meters.

since it takes .1 kilograms of paint to paint 1 square meters, then you need 7.74 * .1 = .774 kilograms of paint to paint all 10 cylinders. *********

this is the same answer we got above with a lot less hassle because we did all the conversions up front.

i can do them both ways, but i've found that doing the conversions up front can save you more time and confusion later on as long as you did the conversions correctly.

i still do them both ways just to make sure i've done them correctly.
if the answers match, then i'm confident i did them correctly.
if not, then i go back and find out where i went wrong.

if this is where you're problem is, then just work with conversions repeatedly until you get a system down that works for you.

once you've got a system down, they should flow more easily.

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