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Cody started a fire in a field. The fire was expanding outward in all directions forming a larger and larger circle. The radius of the circular fire was 10 feet and was increasing at 2 feet/minute when Cody called the fire department. How many minutes will it take from the time Cody called the fire department until the area of the circular fire is 45401 square feet? Type your answer to the nearest hundredth (2 decimal places).

Respuesta :

samuelonum1

Answer:

55.10min

Step-by-step explanation:

This problem is on the mensuration of flat shapes.

given that the initial radius before Cody alerted the fire department is

10 ft

Then we can calculate the area of the fire as

Area= πr^2

Area=3.142*(10)^2

Area=3.142*100

Area=314.2ft^2

Also, given that the area of the circular fire has grown to 45401 square feet

let us solve for the radius first, then we can calculate the time taken since the radius was increasing by 2 ft/min

let the radius of the large fire be R

45401=πR^2

R^2=45401/3.142

R^2=14449.714

square both sides we have

R=√14449.714

R=120.2ft

The difference between the radius of the initial fire and the large fire is

R-r=120.2-10

    =110.2ft

Hence the time taken can be calculated as

time= 110.2/2

time=55.10min