nikki50 said:
I have no possible clue of doing this except a formula for surface area and i don't think it is right but anyway here's the problem.
Problem: You have been hired to paint a historic water tower green. The tower has a cylindricial base that is 12 feet AROUND and 85 feet HIGH. the top is a sphere and is 300 feet AROUND. One Gallon of paint covers 200 square feet and cost about $35 per gallon. HOW MUCH WOULD IT COST TO PAINT THE ENTIRE WATER TOWER?
You are not going to paint the top or the bottom of the cylinder.....you'll be painting the LATERAL AREA of that cylinder. For a cylinder,
Lateral Area = (circumference of base) * height
You're told that the base is a cylinder that is 12 feet AROUND....that's the circumference of the cylinder, and the height of the cylinder is 85 feet. So,
LA = 12 feet * 85 feet
For the sphere on top, you'll need the formula for the surface area of a sphere:
Surface Area = 4*pi*r[sup:1o2qujbb]2[/sup:1o2qujbb]
Oh...but that formula requires the RADIUS of the sphere, and you aren't told that! But, you know that the distance around the sphere is 300 feet, and that is the circumference. For a sphere, like a circle,
C = 2 * pi * r
Ok...so
300 = 2*pi * r
Divide both sides by 2*pi, and you get
300/(2*pi) = r
You can substitute 300 /(2*pi) for "r" in the formula for the surface area of a sphere:
SA = 4 * pi * [300 / (2*pi)][sup:1o2qujbb]2[/sup:1o2qujbb]
As you've been told earlier, there's a small portion of the sphere that's "inside" the cylindrical base. Personally, I think that the radius of the base is so small in comparison to the radius of the sphere on top that it won't make a very big difference in the amount of paint required. Opinions on this will vary, I'm sure.
Anyway...find the area of the sphere and add it to the area of the cylinder to get the total surface area that needs to be painted.
A gallon of paint covers 200 sq. feet....so you'll need to divide the total surface area of the water tower by 200 to find the number of gallons of paint needed (and remember that you can't buy PART of a gallon of paint, so round the number of gallons to the next highest whole number).
Finally, each gallon costs "about" $35....multiply the number of gallons by $35 to find the cost.
The fact that it says "about $35" tells me that we don't need to be too terribly "picky" about that little part of the spherical top that won't get painted.
