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3 years ago

A cylinder has a volume of 198 cm3, and its base has an area of 22 cm2. What is the height of the cylinder? V= πr²h

Mathematics

1 answer:

DIA [1.3K]3 years ago

8 0

Answer:

The height of cylinder is 9 cm

Step-by-step explanation:

Volume of cylinder = 198 cm³

Base Area = 22 cm²

We need to find height of the cylinder

The formula used is: $Volume\:of\:cylinder=\pi r^2h$

Where $Base\: Area = \pi r^2$

First we need to find radius r

$Base\: Area = \pi r^2\\22=3.14\: r^2\\r^2=\frac{22}{3.14}\\r^2=7\\Taking\: square\: root\: on\: both\: sides\\\sqrt{r^2}=\sqrt{7}\\r=2.656$

So, we get radius r = 2.656

Putting values of volume and radius are to find height

$Volume\:of\:cylinder=\pi r^2h\\198=3.14(2.656)^2h\\h=\frac{198}{22}\\h=9$

So, the height of cylinder is 9 cm

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3 years ago

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3 years ago

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3 years ago

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MissTica

Answer:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

We need to find the degrees of freedom given by:

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Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average is higher than 52 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=54.98$ represent the sample mean

$s=8.43$ represent the sample deviation

$n=26$ sample size

$\mu_o =52$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 52, the system of hypothesis would be:

Null hypothesis: $\mu \leq 52$

Alternative hypothesis: $\mu > 52$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{54.98-52}{\frac{8.43}{\sqrt{26}}}=1.8025$

P-value

We need to find the degrees of freedom given by:

$df = n-1= 26-1 = 25$

Since is a right tailed test the p value would be:

$p_v =P(t_{25}>1.8025)=0.0418$

Conclusion

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3 years ago

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