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 inch diameter, and an average fisher has about 500 buoys. A quart of marine paint covers 175 ft squared. How many quarts of paint does an average fisher need each year?

Question

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 inch diameter, and an average fisher has about 500 buoys. A quart of marine paint covers 175 ft squared. How many quarts of paint does an average fisher need each year?

Answer 1

And I forgot to square the radius.

SA = 4 * 3.14 * 0.5^2

SA = 3.14 square feet

(500 * 3.14)/175 = 8.97 = 9 quarts

Answer 2

You're welcome. Sorry about the mixup.

Answer 3

To find out how many quarts of paint an average fisher needs each year, we need to calculate the total surface area of all the buoys and then divide it by the coverage area of paint per quart.

1. Find the surface area of one buoy:
The buoy is a sphere, and the formula for the surface area of a sphere is given by:
Surface Area = 4πr², where r is the radius of the sphere.

Given that the buoy has a diameter of 12 inches, the radius (r) can be calculated by dividing the diameter by 2:
r = 12 inches / 2 = 6 inches.

Now we can calculate the surface area of one buoy:
Surface Area = 4π(6 inches)²

2. Calculate the total surface area of all the buoys:
Since an average fisher has about 500 buoys, we multiply the surface area of one buoy by the number of buoys:
Total Surface Area = 500 × Surface Area of one buoy

3. Convert the surface area to square feet:
The surface area was initially calculated in square inches, but the paint coverage is given in square feet. We need to convert the surface area to square feet to match the paint coverage.

We know that 1 square foot is equal to 144 square inches, so we can convert the surface area:
Total Surface Area (in square feet) = Total Surface Area (in square inches) / 144

4. Determine the number of quarts of paint needed:
Given that 1 quart of paint covers 175 square feet, we can divide the total surface area by the paint coverage per quart:
Number of Quarts = Total Surface Area (in square feet) / Coverage Area per Quart

Now we can compute the answer using the above steps.

Answer 4

Let's change the inches to feet.

SA = 4 * 3.14 * 0.5^2
SA = 6.28 sq. feet

(500 * 6.28)/175 = 17.94 = 18 quarts

Answer 5

area of 1 buoy: pi d^2 = 144pi

so, quarts of paint:

q = 144pi * 500 / 175

Answer 6

And I forgot to square the radius.

Thanks!

You're welcome. Sorry about the mixup.

To find out how many quarts of paint an average fisher needs each year, we need to calculate the total surface area of all the buoys and then divide it by the coverage area of paint per quart.

Let's change the inches to feet.

area of 1 buoy: pi d^2 = 144pi

oops - Go with Ms Sue - I forgot to change inches to feet.