All categories

3 years ago

A cylinder has a base diameter of 8ft and a height of 20ft. What is its volume in cubic ft, to the nearest tenths place?

Mathematics

1 answer:

jenyasd209 [6]3 years ago

5 0

Answer:

$4022.9$

Step-by-step explanation:

Volume of a cylinder is given by cross sectional area multiplied by height hence

V=Ah

Since the cross sectional area of

$A=\pi r^{2}$

Substituting the formula for A into formula for volume then

$V=Ah=\pi r^{2}h$

Substituting 8ft for r and 20 ft for h then

$V=Ah=\pi 8^{2}\times 20=4022.8571428571\ ft^{3}\approx 4022.9\ ft^{3}$

Rounded off to the nearest tenths, the volume is equivalent to

$4022.9$

You might be interested in

Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

2 years ago

A student in a wildlife biology class wants to determine the abundance of a rodent species in a local nature preserve, divided i

LekaFEV [45]

Answer:

c. Cluster sampling

Step-by-step explanation:

Taking into account that the exercise researcher is looking with limited resources to study a population that is divided, her best option is cluster sampling, which is a method applicable to this type of population, we could select in each group randomly her sample, the observational study is discarded because she does not have much availability of time or resources, nor would the stratified study be useful because she should select subgroups and create them to take samples and this would take more time and resources and sampling systematic is not adequate because it must have all the individuals and after having the list select the sample, but as we know, it is a process that will study the number of individuals so this option is not feasible.

5 0

3 years ago

Read 2 more answers

What times 3 equals 3/10

Mumz [18]

Answer:

1/10

Step-by-step explanation:

Divide 3/10 by 3. Remember to "keep, flip, change".

3/10 ÷ 3/1

3/10 × 1/3

Multiply across: 3/10 × 1/3 = 3/30

Simplify: 3/30 = 1/10

7 0

3 years ago

Which of these sets of angle measures could be the three angles in a triangle?

Lady_Fox [76]

Answer:

Okay so this is simple addition, once you know how to do it.

The interior angles of a triangle should always add up to 180 Degrees.

Now that you know this, all you have to do is add the numbers together and see which ones add up to 180 degrees.

A. - 90+42+58=190

B. - 60+60+60=180

C. - 100+48+42=190

D. - 31+75+70=176

Out of these choices the only one that adds up to 180 is B. So your answer would be B.

Read more on Brainly.com - brainly.com/question/2547568#readmore

Step-by-step explanation:

7 0

3 years ago

A plane begins to descend from a height of 202 meters. The plane decreases in altitude at an average rate of 1.8 meters per seco

stepladder [879]

The plane starts at 202 m.
All altitudes are in meters.
After 1 second, it is at 202 - 1.8
After 2 seconds, it is at 202 - 1.8 * 2
After 3 seconds, it is at 202 - 1.8 * 3
etc.
After x seconds, it is at 202 - 1.8 * x

202 - 1.8 * x is the same as 202 - 1.8x

Answer: F. t(x) = 202 - 1.8x

3 0

3 years ago