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Morgarella [4.7K]
3 years ago
6

If you doubled the radius of a sphere, how would the surface area change?

Mathematics
2 answers:
noname [10]3 years ago
3 0
The area scale factor is the length scale factor squared. The length scale factor in this question is 2 (from the doubled radius) so the area scale factor is 2 squared, 4. This means that the surface area will be 4 times larger than it was originally.
Nuetrik [128]3 years ago
3 0

Answer:

The area will get quadrupled that is four times.

Step-by-step explanation:

Surface area of sphere, A = 4πr²

If you doubled the radius of a sphere how would the surface area change.

New radius = 2r

New surface area of sphere, A' = 4π x (2r)²=16πr² = 4A

So the area will get quadrupled that is four times.

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Answer:

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Step-by-step explanation:

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6 0
2 years ago
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.
valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.85}{2} = 0.075

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.075 = 0.925, so Z = 1.44.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

A previous study found that for an average family the variance is 1.69 gallon?

This means that \sigma = \sqrt{1.69} = 1.3

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

M = z\frac{\sigma}{\sqrt{n}}

0.14 = 1.44\frac{1.3}{\sqrt{n}}

0.14\sqrt{n} = 1.44*1.3

\sqrt{n} = \frac{1.44*1.3}{0.14}

(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2

n = 178.8

Rounding up

A sample of 179 is needed.

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