A water treatment facility operates by dripping water from a 70 foot long arm whose end is mounted to a central pivot. The water then filters through a layer of charcoal. The arm rotates once every 6 minutes. (Round your answers to two decimal places.) (a) Find the area of charcoal covered with water after 1 minute ft2 (b) Find the area of charcoal covered with water after 1 second ft2 (c) How long would it take to cover 100 square feet of charcoal with water? sec (d) How long would it take to cover 3445 square feet of charcoal with water?

Question

Mathematics

Alexis Wall

4 October, 23:48

A water treatment facility operates by dripping water from a 70 foot long arm whose end is mounted to a central pivot. The water then filters through a layer of charcoal. The arm rotates once every 6 minutes. (Round your answers to two decimal places.) (a) Find the area of charcoal covered with water after 1 minute ft2 (b) Find the area of charcoal covered with water after 1 second ft2 (c) How long would it take to cover 100 square feet of charcoal with water? sec (d) How long would it take to cover 3445 square feet of charcoal with water?

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Answers (1)

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Chloe Kline · Answer 1

A) the area of charcoal covered with water after 1 minute in ft^ (2) = 1309 ft^ (2)

B) the area of charcoal covered with water after 1 second (in ft^2) = 21.82 ft^ (2)

C) time it would take to cover 100 square feet of charcoal with water (in sec) = 4.58 seconds

D) time it would take to cover 3445 square feet of charcoal with water =

2 min 37.8 seconds

Step-by-step explanation:

A) To find the area of charcoal covered with water after 1 minute in ft^ (2); let's determine area that is covered by 1 rotation of the arm.

radius (r) = 50 ft

area (A1) = πr^ (2) = 3.14 x 50^ (2) = π x 2500 = 7853.98 ft^ (2)

Now, from the question, it takes the arm 6 minutes to rotate once.

hence, the area of charcoal covered with water after 1 minute can be found by dividing the total area by 6;

A1/6 = 7853.98/6 = 1309 ft^ (2)

B) Now, to find the area of charcoal covered with water after 1 second (in ft^2);

We know that there are 60 seconds in 1 minute, thus we simply divide answer in a above by 60.

= A1/60 = 1309.00/60

A2 = 21.82 ft^ (2)

(c) Now, let's find how long it would take to cover 100 square feet of charcoal with water (in sec)

= 100 ft^2 / 7853.98 ft^2 = 0.0127

We know that 6 min = 360 sec

Thus; 0.0127 x 360 sec = 4.58 sec

(d) Now, we'll find how long it would take to cover 3445 square feet of charcoal with water?

3445 ft^2 / 7853.98 ft^2 = y / 6 min = y / 360 sec

7853.98y = 360 x 3445

7853.98y = 1,240,200

y = 1,240,200 / 7853.98

y = 157. 91sec = 157.91/60 = 2.63min = 2 min 37.8 seconds