A circular tunnel, 20 m in diameter is blasted through a mountain. A 16 m wide road isto be constructed along the floor of the tunnel. What is the maximum height of the tunnel to the nearest meter?

To find the maximum height of the tunnel, we need to understand the relationship between the diameter of the tunnel and its height. Let's break down the problem step by step:

1. Start with the diameter of the tunnel, which is given as 20 m.
2. The road width is 16 m. Since the road is constructed along the floor of the tunnel, the height of the tunnel will be equal to the remaining space above the road.
3. To calculate the height, subtract the road width from the diameter: 20 m - 16 m = 4 m.
This result gives us the height from the road to the ceiling of the tunnel.
4. However, we need to find the maximum height, which is the distance from the road to the highest point of the tunnel's curved ceiling.
5. For a circular tunnel, the highest point is located at the center. So, we need to find the distance from the center to the road.
6. The radius of the tunnel is half of the diameter. So, the radius is 20 m / 2 = 10 m.
7. Now, subtract the radius from the height above the road to find the maximum height: 4 m - 10 m = -6 m.

Since the result is negative, it means that the tunnel does not have a maximum height above the road. Therefore, the maximum height of the tunnel to the nearest meter is 0 m.

make a diagram

The road of 16 m will be a chord in your circle.
Draw a line from the centre to the end of the chord, that is a radius of 10.
Now you have a right-angled triangle with sides x and 8 and hypotenuse 10
Use Pythagoras, the rest should be easy