SOLUTION: A flower garden is shaped like a circle. Its diameter is 38yd. A ring-shaped path goes around the garden. The width of the path is 5yd.
The gardener is going to cover the path wit
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The gardener is going to cover the path wit
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Question 1198765: A flower garden is shaped like a circle. Its diameter is 38yd. A ring-shaped path goes around the garden. The width of the path is 5yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 7yd2, how many bags does the gardener need? Found 3 solutions by ikleyn, josgarithmetic, math_tutor2020:Answer by ikleyn(52778) (Show Source):
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A flower garden is shaped like a circle. Its diameter is 38yd.
A ring-shaped path goes around the garden. The width of the path is 5yd.
The gardener is going to cover the path with sand.
If one bag of sand can cover 7yd2, how many bags does the gardener need?
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The area of the ring-shaped path is the difference of the areas
of the larger and smaller circles. So we write
the area of the ring-shaped path = - = = 675.1 yd^2.
To determine the number of bags, we divide it by 7 yd^2
= 96.44
and round it to the closest greater integer, which is 97.
ANSWER. The gardener needs 97 bags of sand.
The garden, minus the path, has a diameter of 38 yards.
Half of which is 38/2 = 19 yards.
This is the radius of the smaller inner circle.
Let's compute the area of this circle
A = pi*r^2
A = pi*19^2
A = pi*361
A = 361pi
The path around the garden is 5 yards in width.
This will add 5 to the radius we found earlier.
19+5 = 24
The outer concentric circle has a radius of 24 yards.
The larger circle has an area of:
A = pi*r^2
A = pi*24^2
A = pi*576
A = 576pi
Now compute the difference of these items to find the area of the garden path only (i.e the outer ring).
576pi - 361pi = (576-361)pi = 215pi
The exact area of the path only is 215pi square yards.
This is approximately
215*3.1415926535898 = 675.442420521807 square yards.
x = number of bags of sand needed
1 bag covers 7 square yards
x bags cover 7x square yards
7x = 675.442420521807
x = 675.442420521807/7
x = 96.4917743602581
Round that up to the nearest integer to get x = 97
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