A single lane street 10 ft wide goes through a semicircular tunnel at the edge of each lane? Round off 2 decimal places
You did not write the radius of the tunnel.
The equation of circle in the tunnel is:
x² + y² = r²
y = the height of the tunnel
r = the radius of the tunnel.
The intersection of the circle and x = 10 / 2 ft , x = 5 ft
x² + y² = r²
5² + y² = r²
25 + y² = r²
Subtract 25 to both sides
y² = r² - 25
y = √ ( r² - 25 )
and round on 2 decimal places
To find the circumference of a semicircle, we can use the formula:
Circumference = π * radius
In this case, the radius of the semicircular tunnel is half of the width of the lane, which is (10 ft) / 2 = 5 ft.
So, the circumference of the semicircular tunnel is:
Circumference = π * 5 ft = 15.71 ft (rounded to 2 decimal places).
Therefore, the circumference of the semicircular tunnel is approximately 15.71 ft.
To find the area of the semicircular tunnel, you need to know the diameter of the tunnel or the radius.
Given that the street is 10 ft wide, we can assume the diameter of the tunnel is equal to the width of the street, which means the radius is half of the width, or 10/2 = 5 ft.
Now, to calculate the area of a semicircle, you can use the formula: Area = (π * r^2) / 2, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius.
Plugging in the values, we get: Area = (3.14159 * 5^2) / 2 = (3.14159 * 25) / 2 = 78.53975 / 2 = 39.26988.
Rounding off to 2 decimal places, the area of the semicircular tunnel is approximately 39.27 square feet.