Question

A flower garden is shaped a diameter is 34 yd A ringshaped path goes around the garden The width of the path is 5yd The is going to cover the path with sand. If one bag of sand can cover 6 ydhow many bags of sand does the gardener need? Note that sand comes by the bagthe number of bags must be a number Use the value 3.14 for

Answer 1

To solve this, we need to find the area of the ring-shaped path. We can find this area, by calculating the area of the whole circular garden and subtracting the area of the flower garden.

The whole garden has a diameter of 34yd for the flower garden, plus the ring-shaped path, which adds 10yd to the diameter, making a total of 44yd diameter circle.

The formula for the area of a circle is:

`A=\pi r^2`

Where r is the radius,

Let's find the area of a circle of diameter 44yd. The radius is half the diameter, thus r = 22

`Area\text{ }whole\text{ }garden=\pi\cdot22^2=3.14\cdot484=1519.76\text{ }yd^2`

And now, the area of the garden without the ring-shaped path. This is a circle of diameter 34yd. Thus, the radius is 17yd.

`Area\text{ }without\text{ }path=\pi\cdot17^2=3.14\cdot289=907.46\text{ }yd^2`

If we now rest the area of the smaller circle to the area of the bigger circle, we get the area of the path:

`Area\text{ }ring-shaped\text{ }path=1519.76-907.46=612.3\text{ }yd^2`

And to find out how many bags of san are needed, we divide the area of the path (612.3 sq yd) by the area that a single bag can cover (6 sq yd):

`(612.3)/(6)=102.05`

Since we can't buy a fraction of a bag,

The answer is 103 bags of sand.