Question

if any one could please help me that would be amazing, thank you!!
Lobster fishers in Maine often use spherical buoys to mark their lobster traps. Every year the buoys must be repainted. An average buoy has a 12 in. diameter, and an average fisher has about 500 buoys. A quart of marine paint covers 175 ft^2. How many paint does an average fisher need each year?

Please help me anyone, thank you!

Answer 1

The surface area of a sphere is \[A=4\pi(r ^{2})\]r=1/2 the diameter.

So we have \[A=4(\pi)(6^{2})\] So one buoy has 452 sq.inches of surface area to paint

Since there are 500 buoys then 452 sq. inches times 500 is the total surface area that needs painting.

500(452)= 226,196 sq. inches.

Since the paint is in sq. ft., we need to change sq. ft into sq. inches.

So we have (175 ft x ft)(12inches/ft)(12 inches/ft) The ft. cancel out. Given us:

175(12)(12)= 25,200 sq. inches So a quart of paint will cover 25,200 sq.inches.

Since we have 226,196 sq. inches to paint, we divide 226,196 by 25,200. Which gives us

226,196/25,200 = 8.97 quarts of paint. We can round that to 9 quarts of paint, since they sell paint in quarts.