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A parabolic tunnel has a width of 20 feet and a height of 12 feet at the center. Find the cross-sectional area of the parabolic tunnel

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Ellakatie18go

Answer:

Q. A tunnel is in the shape of a parabola. If the tunnel is 40 feet wide and has a maximum height of 12 feet, what is the equation of the quadratic function that represents the tunnel? Let the axis of symmetry be the y-axis.

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LucySpearsgo

Question:

♦A parabolic tunnel has a width of 20 feet and a height of 12 feet at the center. Find the cross-sectional area of the parabolic tunnel?

Answer:

The cross-sectional area of the parabolic tunnel is 31415.93 ft²

What is a parabolic tunnel?

A parabolic tunnel assumes the shape of a hemisphere and the cross-sectional area of a hemisphere can be calculated by using the formula:

Area of a parabolic tunnel = πa²

Since the parabolic tunnel assumes the shape of a hemisphere:

♦Radius of the hemisphere from the center = a = 20/2 = 10

♦Height of the hemisphere r = 12

♦Area of a parabolic tunnel = πa²

♦Area of a parabolic tunnel = π(100)²

♦Area of a parabolic tunnel = 31415.93 ft²

Explanation:

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