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

Mathematics

1 answer:

loris [4]2 years ago

4 0

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

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