Multiple choice

In a scientific experiment, researchers are examining a cylindrical chamber. If the radius of the chamber is increased by 20% and the height is decreased by 10%, resulting in an increase in volume of 296 cubic units, what is the original volume of the cylindrical chamber?

  1. 1,000 cubic units

  2. 1,184 cubic units

  3. 1,328 cubic units

  4. 1,472 cubic units

  5. 1,616 cubic units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let V = pi*r^2*h. The new volume is pi*(1.2r)^2*(0.9h) = pi*1.44*r^2*0.9*h = 1.296*V. The increase is 0.296*V = 296, so V = 1,000.

AI explanation

The new radius becomes 1.2 times the original, and the new height becomes 0.9 times the original. The new volume is 1.2 squared times 0.9, which equals 1.44 times 0.9, resulting in 1.296 times the original volume. This represents a 29.6 percent increase in volume, which is given as an increase of 296 cubic units. Setting 0.296 times the original volume equal to 296 and solving gives an original volume of 1,000 cubic units.

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