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creativ13 [48]
2 years ago
6

If a large Rubik's cube has a volume of 1,331 cubic inches what is its surface area?

Mathematics
1 answer:
Blababa [14]2 years ago
5 0
V=(4/3)pir^3
SA=4pir^2

so

given
v=1331
1331=(4/3)pir^3
times both sides by 3/4
998.25=pir^3
divide both sides by pi
998.25/pi=r^3
cube root both sides
∛(998.25/pi)=r

ok
SA=4pir^2
SA=4pi(∛(998.25/pi))²
SA=4pi(∛(996503.0625/(pi²)))
SA=4pi∛(996503.0625/(pi²))
use your calculator
SA=585.15307930795 in²

its surface area is about 585 in²
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Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

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The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

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Since the new Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Assuming that the deviation is known we can express the margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

Replacing into formula (b) we got:

n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

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