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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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Use multiplication to find three ratios equivalent to 8:12

tatyana61 [14]

Ok so 8:12 can be 8 to 12, or 8\12

do that help?

4 0

3 years ago

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Based on the data in this two-way table, which statement is true? A. a flower being pink and a flower being a rose are independe

Goryan [66]

The question is asking to choose among the following choices that state the fact about the said data in the tables, and according to the given data, I would say that the answer would be letter <span>A. a flower being pink and a flower being a rose are independent of each other. I hope this would help </span>

5 0

3 years ago

Add the following polynomials, then place the answer in the proper location on the grid.

WARRIOR [948]

Answer: - 2.4x^2 - 1.5x - 11.4

Step-by-step explanation:

- 4.1x^2 + 0.9x - 9.81.7x^2 - 2.4x - 1.6 = - 2.4x^2 - 1.5x - 11.4

6 0

2 years ago

Baby A and Baby B are born at the same time, and their lengths are recorded after each week. Which statement is true about their

bazaltina [42]

Answer:

A

Step-by-step explanation:

Go to the graph at 12 weeks and the line for Baby A is above Baby B.

8 0

3 years ago

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