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In the early stages of building the Hoover Dam diversion tunnels were built to divert the flow of water away from the main construction site. Each diversion tunnel was cylindrical with a radius of 56 feet and a length of 4,000 feet. Find the volume and surface area of a diversion tunnel.

User Touko
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7 votes

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.

User Youngrrrr
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