Acircular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for pi

178.98

step-by-step explanation:

to find the area of just the path first find the area of the path and the garden combined (the entire big circle):

    area of a circle = 3.14 * r^2

    the radius (r) for the entire big circle is 8 + 3 which is 11

    plug in 11:

        3.14 * 11^2 = 379.94

now you must subtract the area of the garden to find the area of only the path

    start by finding the area of the garden

        3.14 * 8^2 = 200.96

    now subtract the area of the whole big circle by the area of the garden:

          379.94 - 200.96 = 178.98

the second option

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west