Question

A circular path 3 feet wide has an inner diameter of 450 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to nearest hundredth. Use 3.14 for π.

Answer 1

18.84 feet farther is it around the outer edge of the path than around the inner edge.

Given:

A circular path 3 feet wide has an inner diameter of 450 feet.

Use 3.14 for
`\pi`.

Now, to find how much farther is it around the outer edge of the path than around the inner edge.

Width of the circular path = 3 feet.

Inner diameter of circular path = 450 feet.

So, to get the inner radius we divide the inner diameter of circular path by width of circular path:

`450/3`

`=150 \ \text{feet}`

`\text{r} = 150 \ \text{feet}`.

Now,

Thus, the outer radius is:

`150+3`

`=153 \ \text{feet}`

`\text{r} = 153 \ \text{feet}`.

Now, we get the circumference of inner edge and outer edge:

`\bold{Circumference \ of \ inner \ edge} = \bold{2\pi r}`

`\text{Circumference of inner edge} = 2*3.14*150`
`\text{Circumference of inner edge}=942 \ \text{feet}.`

`\bold{Circumference \ of \ outer \ edge} = \bold{2\pi r}`

`\text{Circumference of outer edge} = 2*3.14*153`

`\text{Circumference of outer edge}=960.84 \ \text{feet}.`

Now, to get how much farther is it around the outer edge of the path than around the inner edge:

`\text{Circumference of outer edge - circumference of inner edge}`.

`960.84-942`

`=18.84 \ \text{feet}.`

Therefore, 18.84 feet farther is it around the outer edge of the path than around the inner edge.