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Square Yards, Area

 
 
Reply Thu 29 Jan, 2015 08:30 pm
In a park is a circular lake 240' in diameter with a walkway 6' in width around the lake. Calculate amount of square yards in walkway. Calculate area of walkway if width is doubled.


Area of ring - pi(R + r) (R - r)

A = pi(120 + 3) (120 - 3)
A = pi(123) (117)
A = pi (14391)
A = 3.1416 (14391)
A = 45210.7656 square yards

How do I proceed from here ?



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raprap
 
  1  
Reply Thu 29 Jan, 2015 09:13 pm
Check your units. The diameter of the lake and the walk is in feet.

Rap
0 Replies
 
engineer
 
  1  
Reply Thu 29 Jan, 2015 09:18 pm
@Randy Dandy,
You are using the wrong formula for the area of the walkway.

Area of ring = pi ( (R+r)^2 - R^2)

Also as Rap mentioned, there are 9 sq ft per sq yd.
Randy Dandy
 
  1  
Reply Thu 29 Jan, 2015 10:35 pm
@engineer,
Pi(R^2 - r^2)
Pi(120^2 - 3^2)
Pi(14400 - 9)
Pi(14391)
3.1416(14391)
45210.7656 = 45211 square feet

452111/9 = 5023.444= 5023 square yards

??
engineer
 
  1  
Reply Fri 30 Jan, 2015 11:43 am
@Randy Dandy,
Read the formula again.

Pi ( 123^2 - 120^2)
Randy Dandy
 
  1  
Reply Fri 30 Jan, 2015 02:38 pm
@engineer,
Pi (123^2 - 120^2)
Pi (15129 - 14400)
Pi (729)
3.1416 (729)
2290.2264 = 2290 square feet
2290/9 = 254.444 = 254 square yards

How do I proceed from here?
engineer
 
  1  
Reply Fri 30 Jan, 2015 02:49 pm
@Randy Dandy,
First, I made a mistake and we need to correct it. The radius of the lake is indeed 120, but the radius of the outer circle is not 123, it is 126. The walkway is 6 feet in width, you don't need to half it, so use

Pi (126^2 - 120^2) for the area but otherwise your answer is correct.

For the second part where the walkway is doubled in width, do the same thing but use 132 for the outer radius.
Randy Dandy
 
  1  
Reply Fri 30 Jan, 2015 03:41 pm
@engineer,
Pi (132 ^2 - 120 ^2)
Pi (17424 - 14400)
Pi (3024)
3.1416 (3024)
9500.1984 = 9500 square feet
9500/9 = 1055.555 = 1056 square yards
0 Replies
 
 

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