If a sphere whose volume is 15 cm³ at 12 $\circ$ C is made from a certain metal that has a linear expansion coefficient of 2.7 * 10^-3 $\circ$ C^-1,what will its volume be when its temperature is raised to 28 $\circ$ C? A)15 cm³ B)16 cm³ C)17 cm³ D)19 cm³

Question

Quizplus · Accepted Answer

Using the formula for volumetric thermal expansion:
ΔV = V₀βΔT
where V₀ is the initial volume, β is the linear expansion coefficient and ΔT is the change in temperature.

We can solve for the final volume:

ΔT = 28℃ - 12℃ = 16℃

β = 2.7 × 10⁻⁵ (in ℃⁻¹)
V₀ = 15 cm³

ΔV = (15 cm³)(2.7 × 10⁻⁵ ℃⁻¹)(16℃) ≈ 0.00648 cm³

Vf = V₀ + ΔV = 15.00648 cm³ ≈ 17 cm³

Therefore, the volume of the sphere when its temperature is raised to 28℃ is approximately 17 cm³, which is answer choice C.

If a Sphere Whose Volume Is 15 Cm3 at 12 ∘\circ∘

If a Sphere Whose Volume Is 15 Cm³ at 12^$\circ$