Multiple choice

A cone with a base radius of 6 cm and a height of 12 cm is placed upside down in a cylindrical container. The cylindrical container has a diameter of 14 cm and a height of 15 cm. What is the remaining volume of the cylinder after the cone is placed inside it?

  1. 540π cm3

  2. 591π cm3

  3. 915π cm3

  4. 951π cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cylinder volume = pi * r^2 * h = pi * 7^2 * 15 = 735pi. Cone volume = (1/3) * pi * r^2 * h = (1/3) * pi * 6^2 * 12 = 144pi. Remaining volume = 735pi - 144pi = 591pi.

AI explanation

We first find the volume of the cylindrical container using the formula pi times the square of the radius times the height, using the radius of 7 cm to get pi times 7 squared times 15, which equals 735 pi cubic cm. Next, we calculate the volume of the cone using 1/3 times pi times the square of the radius times the height, yielding 1/3 times pi times 6 squared times 12, which equals 144 pi cubic cm. Subtracting the volume of the cone from the volume of the cylinder gives 735 pi minus 144 pi, resulting in 591 pi cubic cm.

Keep practicing — related questions