0 .0346 as a fraction.

The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the

jek_recluse [69]

The biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>

If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is $x$ , the diameter and the height of the cylinder are also $x$
If the side length of a cube is $x$ unit, then its diagonal will be $x\sqrt{3}$ unit.
The formula for the volume of a cylinder is $V=\pi r^2h$ , where $r$ is the radius and $h$ is the height of the cylinder. If $d$ is the diameter, then $r=\frac{d}{2}$ .

Now, given that the diagonal of the cube is $24$ cm. So, if the side length of the cube is $x$ cm, then we must have

$x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}$

Thus, the side length of the cube is $8\sqrt{3}$ cm.

So, the height of the cylinder with maximum volume will be $h=8\sqrt{3}$ cm and the diameter will be $d=8\sqrt{3}$ cm i.e. the radius will be $r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}$ cm.

So, using the above formula for the volume of a cylinder, we get

$V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3$ .

Therefore, the biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

To know more about volume, refer: brainly.com/question/1972490

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4 0

2 years ago

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Topic : Geometry<br> Can someone tell me what analytic geometry is in 4-8 sentences ?

Amanda [17]

Answer:

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics, rocket science etc.

3 0

3 years ago

A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350

tino4ka555 [31]

The 19th generation will be 517262.158012 errr and so on. :3 Hope that helps

3 0

4 years ago

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Daca a/3=7/10 calculati 100a

likoan [24]

A/3=7/10
21=10a
a=2.1
100a=100*2.1=210

6 0

4 years ago

You travel 300 km in a Sierra GMC 4WD truck. Gas costs $1.01/L. The gas mileage

rusak2 [61]

Part A)

The mileage for city use is 16.81 L per 100 km. In other words, if you traveled 100 km in the city, then you use up 16.81 liters of gas.

We can set up this equation

16.81 liters = 100 km

Multiply both sides by 3 so that the "100 km" turns into "300 km"

16.81 liters = 100 km

3*16.81 liters = 3*100 km

50.43 liters = 300 km

<h3>Answer: 50.43 liters</h3>

==================================

Part B)

Multiply the answer in part A by the cost per liter, which is $1.01

Total cost = (cost per liter)*(number of liters)

Total cost = (1.01)*(50.43)

Total cost = 50.9343

Total cost = 50.93

<h3>Answer: 50.93 dollars</h3>

==================================

Part C)

We're effectively repeating part A, but now we're using the highway mileage value.

11.8 liters = 100 km

3*11.8 liters = 3*100 km

35.4 liters = 300 km

<h3>Answer: 35.4 liters</h3>

==================================

Part D)

We follow similar steps as we did in part B. Use the value in part C to get

Total cost = (cost per liter)*(number of liters)

Total cost = (1.01)*(35.4)

Total cost = 35.754

Total cost = 35.75

<h3>Answer: 35.75 dollars</h3>

==================================

Part E)

Subtract the results of parts B and D

50.93 - 35.75 = 15.18

<h3>Answer: 15.18 dollars</h3>

4 0

3 years ago