Answer:
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
Explanation:
To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.
The volume of a cylinder is given by the formula:
V = πr^2h
Where:
V is the volume,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
V = π(56^2)(4,000)
V ≈ 3.14159 * 56^2 * 4,000
Calculating the volume:
V ≈ 9,839,916,800 cubic feet
The surface area of the lateral (curved) part of a cylinder is given by the formula:
A = 2πrh
Where:
A is the surface area,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
A = 2π(56)(4,000)
A ≈ 2 * 3.14159 * 56 * 4,000
Calculating the surface area:
A ≈ 1,000,530.9 square feet
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.