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MAXImum [283]
3 years ago
11

How does the volume of a sphere compare to that of the volume of a cylinder? What would you say the scale factor for Vol sphere:

Vol cylinder
Mathematics
1 answer:
borishaifa [10]3 years ago
3 0

Answer:

The volume of a sphere is 2/3 times the volume of a similar cylinder

Scale factor : 2/3

Step-by-step explanation:

Let us consider a sphere of radius r. The volume of the sphere will be given as

V_{s}=\frac{4}{3} \pi r^{3}

Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:

V_{c}=\pi r^{2}h

but h = 2r

Hence we have

V_{c}= 2\pi r^{3}h

We can divide the two volumes to get a constant that links them together

\frac{V_{s}}{V_{c}}=\frac{\frac{4}{3} \pi r^{3}}{2\pi r^{3}h}

this will give us 2/3

Hence the scale factor for Vol sphere: Vol cylinder is 2/3

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