The Eiffel Tower is a steel structure whose height increases by 19.0 cm when the temperature changes from -9 to +41 oC. What is the approximate height (in meters) at the lower temperature?

To find the approximate height at the lower temperature, we can use the formula for linear expansion. The formula is given as:

ΔL = L₀ * α * ΔT

Where:
ΔL is the change in length
L₀ is the initial length
α is the coefficient of linear expansion
ΔT is the change in temperature

In this case, we are given:
ΔL = 19.0 cm = 0.19 m (converting cm to meters)
ΔT = 41 oC - (-9 oC) = 50 oC (change in temperature)

The coefficient of linear expansion for steel varies, but a common value is α = 12 x 10⁻⁶ oC⁻¹

Let's plug in the values into the formula to find the initial height, L₀:

0.19 m = L₀ * (12 x 10⁻⁶ oC⁻¹) * 50 oC

Simplifying:

L₀ = 0.19 m / (12 x 10⁻⁶ oC⁻¹ * 50 oC)
≈ 0.3167 m

Therefore, the approximate height at the lower temperature is 0.3167 meters.

To find the approximate height of the Eiffel Tower at the lower temperature, we need to consider the change in height due to the change in temperature.

Given:
Change in temperature = +41 oC - (-9 oC) = +50 oC
Change in height = 19.0 cm

To solve this problem, we'll use the coefficient of linear expansion formula:

ΔL = α * L0 * ΔT

Where:
ΔL = change in length or height
α = coefficient of linear expansion
L0 = initial length or height
ΔT = change in temperature

Since the problem states that the Eiffel Tower is made of steel, we need to find the coefficient of linear expansion for steel. The coefficient of linear expansion for steel is approximately 12 x 10^-6 oC^-1.

Now let's solve for the initial height (L0) at the lower temperature:

ΔL = α * L0 * ΔT

Rearranging the formula to solve for L0:

L0 = ΔL / (α * ΔT)

Substituting the known values:

L0 = 19.0 cm / (12 x 10^-6 oC^-1 * 50 oC)

Calculating:

L0 ≈ 3166.67 cm

Converting to meters:

L0 ≈ 31.67 m

Therefore, the approximate height of the Eiffel Tower at the lower temperature is approximately 31.67 meters.