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3 years ago

Find the Volume of the cylinder

Mathematics

1 answer:

JulsSmile [24]3 years ago

8 0

$\huge{\underline{\underline{\sf{\red{Required\:Solution:-}}}}}$

<h3>Volume of cylinder B is greater.</h3>

<h2>For Cylinder A :-</h2>

$\displaystyle{\sf{\:\:\:\:\:\:\:\:r(radius)\:=\: \dfrac{7}{2}cm}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:h(height)\:=\: 14cm}}$

$\displaystyle{\boxed{\sf{ Volume\:=\: \pi r^{2}h}}}$

Substitute the values and simplify it

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:= \dfrac{22}{7} \times \bigg(\frac{7}{2}^{2} \bigg)\times14}}$

$\large{\boxed{\sf{\orange{= 539 cm^{3}}}}}$

<h2>For Cylinder B:-</h2>

$\displaystyle{\sf{\:\:\:\:\:\:\:\:r(radius)\:=\: \dfrac{14}{2}cm=7cm}}$

$\displaystyle{\sf{\:\:\:\:\:\:\:\:h(height)\:=\: 7cm}}$

$\displaystyle{\boxed{\sf{ Volume\:=\: \pi r^{2}h}}}$

Substitute the values and simplify it.

$\displaystyle{\sf{\:\:\:\:\:\:\:\:\:\:= \dfrac{22}{7} \times (7^{2})\times7}}$

$\large{\boxed{\sf{\green{= 1078 cm^{3}}}}}$

<h3>By actual calculation of volumes of both the cylinders, it is verified that the volumes of cylinder B is greater.</h3>

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Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

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Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

$Z = \frac{X - \mu}{s}$

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

$Z = \frac{X - \mu}{s}$

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

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Jennifer wants to rent a car for 5 days, and she’s interested in a the loss damage waiver but not the collision damage wavier.If

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T= total cost
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Total cost equals the cost per day times the number of days plus the fee.

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substitute 5 for n
T= 39(5) + 65
T= 195 + 65
T= $260 total cost

Hope this helps! :)

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3 years ago

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Find the Volume of the cylinder​

Find the Volume of the cylinder