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elixir [45]
2 years ago
12

PLEASE ANSWER A AND B, GIVING BRAINLIEST!

Mathematics
1 answer:
asambeis [7]2 years ago
3 0

Answer:

  a)  V = (8 -4/3π)r³

  b)  2048(2 -π/3) cm³ ≈ 1951.34 cm³

Step-by-step explanation:

When a sphere is placed in a box the empty space volume is the difference between the box volume and the sphere volume. Here, the box is a cube with the same outside dimensions as the sphere.

__

<h3>a. (formula)</h3>

The side length of the cube is 2r, where r is the radius of the sphere. So, the volume of the cube is ...

  V = s³ = (2r)³ = 8r³

The volume of the sphere is given by the formula ...

  V = 4/3πr³

The volume of the empty space is the difference of these:

  V = (8r³) -(4/3πr³)

  V = (8 -4/3π)r³ . . . . . . . formula for the empty volume

__

<h3>b. (empty space)</h3>

For r=8 cm, the empty volume is ...

  V = (8 -4/3π)(8 cm)³ = 4(2 -π/3)(512 cm³)

  V = 2048(2 -π/3) cm³ ≈ 1951.34 cm³ . . . . empty volume

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