A quartz sphere is 14.0 cm in diameter. What will be its change in volume if its temperature is increased by 305 °F? (the coefficient of volume expansion of quartz is (1.50 × 10^-6) °C-1) Answer in cm^3

I tried this twice and got 0.657 cm^3 and 0.18cm^3 but they are both incorrect. Is my third attempt correct?

(100/180) change in C = 1 change in F
305 change in F = 305*(100/180) C = 169.4 change in C

delta V = V1*gamma*dT
= (4/3)*pi*(d/2)^3*gamma*dT
= (4/3)*pi*(0.14/2)^3*1.5*10^-6*169.4
= 0.3650794557

To find the change in volume of a quartz sphere, we can use the equation:

ΔV = V1 * γ * ΔT

where ΔV is the change in volume, V1 is the initial volume, γ is the coefficient of volume expansion, and ΔT is the change in temperature.

Given information:
- Diameter of the quartz sphere = 14.0 cm
- Coefficient of volume expansion of quartz = 1.50 × 10^-6 °C^-1
- Change in temperature = 305 °F

First, let's convert the change in temperature from Fahrenheit to Celsius:
(100/180) ΔT = ΔT_Fahrenheit
(100/180) ΔT = 305
ΔT = 305 * (100/180) = 169.4 °C

Now, let's find the initial volume (V1) of the quartz sphere:
V1 = (4/3) * π * (r^3)
where r is the radius of the sphere.

The diameter of the sphere is given as 14.0 cm, so the radius (r) is half of that:
r = 14.0 cm / 2 = 7.0 cm

Substituting the values into the equation:
V1 = (4/3) * π * (7.0 cm)^3 = 1791.91 cm^3 (approximately)

Now, let's calculate the change in volume:
ΔV = V1 * γ * ΔT
ΔV = 1791.91 cm^3 * (1.50 × 10^-6 °C^-1) * 169.4 °C

Calculating this result gives:
ΔV ≈ 0.365 cm^3

So, it seems your third attempt is correct. The change in volume of the quartz sphere when the temperature is increased by 305 °F is approximately 0.365 cm^3.