George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a.
What is the area of the pool cover?
b.
What is the length of the rope?
as you recall
a = πr^2
c = 2πr
so, the pool with cover has a diameter of 21 ft. The radius is thus 10.5
Now just plug and chug.
Steve it was wrong.
What is the actual answer?
a. To find the area of the pool cover, we can start by calculating the radius of the pool. The radius is half the diameter, so in this case, it will be 20 feet divided by 2, which gives 10 feet.
Next, we need to find the area of the circular pool cover. The area of a circle is calculated using the formula A = π * r^2, where A is the area and r is the radius.
Plugging in the values, we get A = π * 10^2 = 100π square feet.
So, the area of the pool cover is 100π square feet.
b. To find the length of the rope, we need to calculate the circumference of the pool cover. The circumference of a circle can be calculated using the formula C = 2 * π * r, where C is the circumference and r is the radius.
Again, plugging in the values, we get C = 2 * π * 10 = 20π feet.
Since the rope runs along the edge of the cover, its length will be equal to the circumference of the pool cover. Therefore, the length of the rope is 20π feet.