Multiple choice

Calculate the volume of the shell. A hollow spherical shell has inner radius $0.3$ cm and outer radius $0.5$ cm.

  1. $0.410 \space\ cm^3$
  2. $0.310 \space\ cm^3$
  3. $0.210 \space\ cm^3$
  4. $0.110 \space\ cm^3$
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A Correct answer
Explanation

The volume of a spherical shell is (4/3) * pi * (R^3 - r^3). With R=0.5 and r=0.3, volume = (4/3) * 3.14159 * (0.125 - 0.027) = (4/3) * 3.14159 * 0.098 = 0.4105 cm^3.

AI explanation

Using the volume of a spherical shell formula V equals 4/3 times pi times the outer radius cubed minus the inner radius cubed, we substitute the values 0.5 cm and 0.3 cm. This yields V equals 4/3 times pi times (0.5 cubed minus 0.3 cubed), which equals 4/3 times 3.1416 times (0.125 minus 0.027). Calculating this gives 4/3 times 3.1416 times 0.098, resulting in approximately 0.411 cubic cm, making 0.410 cubic cm the closest correct result.

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