Multiple choice

If the radius of a hemi-sphere is reduced by 10% then find percentage change in its volume?

  1. 2.71% decrease

  2. 22.14% increase

  3. 25.2% decrease

  4. 27.1% decrease

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of a hemisphere is proportional to r^3. If r decreases by 10%, the new radius is 0.9r. The new volume is (0.9)^3 = 0.729 of the original volume. The decrease is 1 - 0.729 = 0.271, which is 27.1%.

AI explanation

The volume of a hemisphere formula is V equals 2 over 3 times pi times r cubed, meaning volume depends on the cube of the radius. If the radius is reduced by 10%, the new radius becomes 0.9 times the original, so the new volume is 0.9 cubed, or 0.729, of the original volume. This represents a decrease of 1 minus 0.729, which is a 27.1% decrease.

Keep practicing — related questions