Multiple choice

A metal sphere is heated from $0^{\circ} C$ to $100^{\circ} C$. The change in volume of 10 cm radius is ($\gamma =6.3\times 10^{-5}/^{\circ} C$)

  1. 1026.4cc

  2. 26.4cc

  3. 2.64cc

  4. 264.3cc
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Change in volume = V * gamma * delta_T. V = (4/3) * pi * r^3 = (4/3) * 3.14 * 1000 = 4186.67 cc. Change = 4186.67 * 6.3 * 10^-5 * 100 = 26.376 cc, which rounds to 26.4 cc.

AI explanation

The change in volume due to heating is calculated using the formula delta V = V_initial * gamma * delta T. The initial volume of the sphere with a 10 cm radius is V_initial = (4/3) * pi * r^3 = (4/3) * pi * (10)^3 = 4000 * pi / 3 cc, which is approximately 4188.79 cc. Using the given volume expansion coefficient gamma = 6.3 * 10^-5 / degrees C and temperature change of 100 degrees C, the change in volume is delta V = 4188.79 * 6.3 * 10^-5 * 100 = 26.4 cc.

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