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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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If x and y are positive integers is x - y always positive explain

r-ruslan [8.4K]

Note that x and y are nonzero integers. It means that x and y will always have same sign (both are either positive or negative, since they are nonzero). Hence, xy term is always positive.

3 0

3 years ago

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Solve x^4 y^4=706 given x y=8.........

lapo4ka [179]

<span>Maybe xy is also given ........................</span>

4 0

3 years ago

Solve for 2 unknowns<br> 3y + 3x =24<br> 6y+3x = 39

kari74 [83]

The two unknown variable in the two given equations are "x" and "y".
3y + 3x = 24
Dividing both sides by 3 we get
y + x = 8
x = 8 - y
Putting the value of y in the second equation we get
6y + 3x = 39
Dividing both sides by 3 we get
2y + x = 13
2y + 8 - y = 13
y = 13 - 8
= 5
Putting the value of y in the first equation we get
y + x = 8
5 + x = 8
x = 8 - 5
x = 3
So the value of x is 3 and the value of y is 5. I hope the procedure is clear enough for you to understand.

3 0

4 years ago

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The area of a circle is 28.26 square feet. What is the circle's circumference?

Marina86 [1]

Reverse the formula of pi x r^2 = area to find r, the radius.
Then, use r in the formula 2pi x r to calculate the circumference.

4 0

3 years ago