Please I need any help that I can get on this Geometry question!!!! It's urgent!! I need help immediately!?

Question

I know the answer to this, but I don't understand how to do this or why this is the answer and I need to show my work. Here is the question

You are building a swimming pool in the shape of a circle with a diameter of 28 feet. You also need a deck around the pool that is uniform in width. If the area of the deck is 60(pi sign) square feet, what is the width of the deck?

Please help if you can!!!!!!!

THANKS SO MUCH!!!!!!!!!!!!!!!

Answer 1

Hi,

If the pool in the shape of a circle has a diameter of 28 feet, then its area is πr² = π(14)² = 196π. If the area of the deck is 60π square feet, then the total area of the pool and the deck, is 196π + 60π = 256π.

If a circle has an area of 256π, then A = πr² becomes:

256π = πr²

256 = r²

16 = r

The radius of the deck is 16 feet and the radius of the pool is only 14 feet, so the width of the deck is 16 - 14 = 2 feet as the deck width.

Deck width = 2 feet <==ANSWER

I hope that helps!! :-)

Answer 2

See if this works.

1- Take the diameter and find the area of the pool.  A=r^2(pi) = 196 (pi)

2-Add the area of the deck to the area of the pool.  

196(pi)+60(pi)=256(pi)

3-Find the diameter from the combined area of the pool and deck.

  Formula to find diameter from area is square root (4A/(pi))  

[note: A=area]

sqrt(4(256(pi))/(pi)  = sqrt(1024) = 32.  So the diameter is 32.

4-Subract the diameter of the pool for the total diameter.  32-28=4

5-This means the width of the deck is 4 ft. wide.