Math problem solving help! how to solve step by step? ?

Question

a circular swimming pool, 20ft in diameter, is enclosed by a wooden deck that is 3ft. wide, what is the area of the deck? how much fence is required to enclose the deck?

Answer 1

the area of the swimming pool is pi*r^2=pi*10^2=100pi

the area of the deck is the area of the big circle with radius 3+10 ft minus the area of the pool so we have pi*13^2-100pi=69pift^2

Answer 2

Area of swimming pool=pi(10)^2

Area of deck and swimming pool=pi(13)^2

Area of the deck only=pi(13)^2 - pi(10)^2= 216.66 square feet

The fence required is equal to the circumference of the deck therefore

fence=2pi(13)=81.64 feet

Answer 3

diameter of pool plus deck = 20 + 2×3

= 26 ft

area of pool plus deck = πr²

= π(26/2)²

= 169π ft²

area of pool alone = πr²

= π(20/2)²

= 100π ft²

area of deck = 169π - 100π

= 69π ft²

= 216.8 ft²

perimeter of deck = πd

= π26

= 81.7 ft

Answer 4

Area of the deck:

= (3.14159[{(20 + 6)/2}²]) - (3.14159[{20/2}²])

= (3.14159{26/2}²]) - (3.14159[10²])

= (3.14159[13²]) - (3.14159[100])

= (3.14159[169]) - 314.159

= 530.9287 - 314.159

= 216.7697

Answer: 216.7697 square feet

Circumference of the deck:

= (20 + 6)(3.14159)

= 26(3.14159)

= 81.68134

Answer: 81.68134 feet

Answer 5

The swimming pool is a circle with diameter = 20ft therefore it's radius = 1/2(20)ft = 10ft. The deck is a larger circle that encloses the pool. The 3ft of deck enlarges the diameter of the circle by 6ft because it goes all the way around the pool - adding 3ft on either side of the original diameter. That makes  a diameter of 26 ft, and a radius of 13ft. The formula for the area of a circle is pi r^2 ("pi r squared", where r = radius). In order to get the area of just the deck, you have to calculate the total area (deck + pool) and then subtract the area of the pool. Basically, you are cutting the area of the smaller circle out of the center of the larger circle.

Area of (deck + pool): r = 13, r^2 = (13)^2 = 169. pi = 3.14

pi r^2 = (3.14)(169) = 530.9 sq ft (measured in square feet)

Area of pool: r = 10, r^2 = (10)^2 = 100

pi r^2 = (3.14)(100) = 314.2 sq ft

530.9 sq ft - 314.2 sq ft = 216.7 sq ft.

The area of the deck only = 216.7 sq ft.

The fencing question is a perimeter question. the formula for the perimeter of a circle = 2 pi (r) . This time you are looking for the perimeter of the larger (outer) circle, so you are using r = 13.

P = 2 pi (r)

P = 2 (3.14)(13) = 81.7 ft

Hope that helps you!  

Answer 6

Area of pool = pi x radius^2

radius = diameter/ 2

radius = 20/2 = 10 ft

Area of pool = pi x 10^2

Assume pi = 3.1416

Area of pool = 3.1416 x 100

Area of pool = 314.16 sq. ft.

Area of the deck = Area of the deck and pool MINUS area of pool

Area of deck and pool = pi x radius^2

radius =  10 + 3 = 13 ft

Area of deck and pool = 3.1416 x 13^2

Area of deck and pool = 3.1416 x 169

Area of deck and pool = 530.93 sq. ft

Area of deck = 530.93 - 314.16

Area of deck = 216.77 sq. ft.

Fence to enclose the deck = circumference of the pool and the deck

Circumference = pi x diameter

diameter = 2 x radius

diameter = 2 x 13 = 26 ft

Circumference = pi x 26

Circumference = 3.1416 x 26

Circumference = 81.68 ft

You need 81.68 ft of fence to enclose the deck.

Answer 7

Unfortunately, I can't draw pictures here, so use your imagination.  Here goes:

Think of a circle that is 20 feet in diameter.  Now imagine another circle outside the first circle that is 3 feet wider on each side.  That makes a total of 6 feet bigger in diameter (20 + 3 + 3 = 26).  Think of this as a giant life-saver.  Now to find the area of this deck, all you have to do is take the difference between the area of the bigger circle minus the area of the smaller circle.

The area of a circle is A = π r² where r is the radius (1/2 of the diameter).

The diameter of the bigger circle is 26.  The radius is 13.

The diameter of the smaller circle is 20.  The radius is 10.

The area of the bigger circle = π (13)² = 3.1416 (169) = 530.93

The area of the smaller circle = π (10)² = 3.1416 (100) = 314.16

The difference is the area of the deck = 530.93 - 314.16 = 216.77 ft²

The fence around the deck is the same as the circumference of the bigger circle.  The circumference = π D = 3.1416 (26) = 81.68 ft