Multiple choice

A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

  1. 232

  2. 256

  3. 264

  4. 243
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cone is cut at 18 cm from the base, so the top cone has height 27-18 = 9 cm. The ratio of heights is 9:27 = 1:3. The ratio of volumes is 1^3:3^3 = 1:27. Let total volume be V. Top volume is V/27, bottom frustum is 26V/27. Difference is 25V/27 = 225. V = 225 * 27 / 25 = 9 * 27 = 243.

AI explanation

When the cone is cut 18 cm from the base, the top section has a height of 9 cm, which is one-third of the total 27 cm height. Because volume scales with the cube of the height ratio, the top section is one twenty-seventh of the total volume, making the bottom piece twenty-six twenty-sevenths of the total volume. The difference in their volumes is 25 divided by 27 of the total volume, which we set equal to 225 cc. Solving gives the total volume as 225 times 27 divided by 25, resulting in 243 cc.

Keep practicing — related questions