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I am Lyosha [343]

3 years ago

12

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 m^3. What is the volume of the sphere?

2 answers:

Tamiku [17]3 years ago

5 0

Answer:

C = 128

Step-by-step explanation:

I took the test

Alika [10]3 years ago

3 0

The correct answer is C) 128/3 m^3.

The formula for the volume of a sphere is V=4/3πr³.
The formula for the volume of a cylinder is V=πr²h.

Since the cylinder and the sphere have the same height:

The "height" of the sphere is the same as the diameter. This means the height of the cylinder is equal to the diameter of the sphere, or 2 times the radius:
h=2r

Plugging this into our formula for the volume of a cylinder, along with the actual volume, we have:
V=πr²h
64=πr²(2r)
64=2πr³

Dividing both sides by 2π, we have
64/2π = r³
32/π = r³

Plugging this into our formula for the volume of a sphere:
V=4/3πr³
V=(4/3)π(32/π)
V=128π/3π
V=128/3

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