Pls help am failing <br> Hehehehgshdhdjsjbsvdv

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

1 year ago

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in the san diego zoo there are 4 times as many rabbits as foxes if there are 100 total rabbits and foxes in the zoo how many of

tatiyna

Answer:

100 rabbits

25 foxes

Step-by-step explanation:

Because if there are 100 rabbits, we already know how many rabbits there are so, since we are trying to figure out how many foxes there are we take the 100 ÷ 4 = 25 foxes.

8 0

2 years ago

Suppose you write a sum of numbers as a product of their GCF and another sum. What is the GCF of the number in the other sum? Ex

Fantom [35]

Example :
20 + 30.....GCF = 10

10(2 + 3)

The GCF of the number now is 1....because u have basically already factored the GCF out.....leaving only 1 as a factor now

here's another one...
3 + 9...GCF = 3
3(1 + 3)
so the GCF now is 1

8 0

2 years ago

gina visited the aquarium with some of her cousins aunts and uncles.the group bought 20 admission tickets for $340.adult tickets

jeka94

Answer:

375

Step-by-step explanation:

340 + 20+ 15 = 345

4 0

2 years ago

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What is 10,500,000,000,000,000