Question

Find the volume of the space inside the right cylinder that is not filled by the right cone below.

Answer 1

9514 1404 393

Answer:

  D.  640 m³

Step-by-step explanation:

The height CD of the cone is found using the Pythagorean theorem.

  BC² + CD² = BD²

  8² + CD² = 17²

  CD = √(289 -64) = 15

The volume of the cylinder is ...

  V = πr²h

The volume of the cone is ...

  V = 1/3πr²h

So, the portion of the cylinder not occupied by the cone is ...

  V = (πr²h) -(1/3πr²h) = (2/3)πr²h

  V = 2/3(π)(8 m)²(15 m) = 640π m² . . . . . matches choice D