Anna is covering a circular pool with a cover for winter. The pool's diameter is 24 feet. The cover extends 12 inches beyond the edge of the pool, and a rope runs along the edge of the cover to hold it in place. What is the area of the cover? What is the length of the rope.
I know how to find area of a circle (formula is A=pi times the radius squared) but I don't know how to find the diameter of of the cover because 12 inches are added. Also, I am kinda lost on how to find the length of the rope because I'd have to find the diameter of the cover first I think. P.S. Radius is half the diameter.
Thanks for your help
just add 6 inches to the radius
To find the area of the cover, we first need to determine the diameter of the cover considering the additional 12 inches.
Given that the pool's diameter is 24 feet, we can determine the diameter of the cover by adding the extra 12 inches on both sides. Since there are 12 inches in a foot, the additional length is 12/12 = 1 foot.
So, the diameter of the cover is 24 feet + 1 foot = 25 feet.
Now that we have the diameter, we can calculate the radius of the cover by dividing the diameter by 2. The radius is 25 feet / 2 = 12.5 feet.
To find the area of the cover, we can use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
Plugging in the values, we get A = π * (12.5 feet)^2.
Calculating this, the area of the cover is approximately 490.87 square feet.
Now, let's move on to finding the length of the rope.
The rope runs along the edge of the cover, which is the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Plugging in the values, we get C = 2π * 12.5 feet.
Calculating this, the length of the rope is approximately 78.54 feet.