what is the volume of a regular octahedron inside a cube with the length of its sides measuring 4 centimeters ​

Answers

Answer 1

Answer:

We conclude that the volume of a regular octahedron will be:

[tex]\:\:V\:\approx \:30.17[/tex] cm

Step-by-step explanation:

Given

The length of one of the side or edge of a regular octahedron = a = 4 cm

To determine

The volume of a regular octahedron = V

Using the formula to determine the volume of a regular octahedron

[tex]V\:=\:\frac{\sqrt{2}}{3}a^3[/tex]

substituting a = 4 in the volume equation

[tex]V=\frac{\sqrt{2}\cdot \:4^3}{3}[/tex]

[tex]V=\frac{64\sqrt{2}}{3}[/tex]         ∵ 4³ = 64

[tex]\:\:V\:\approx \:30.17[/tex] cm

Therefore, we conclude that the volume of a regular octahedron will be:

[tex]\:\:V\:\approx \:30.17[/tex] cm

Related Questions

Hem dibuixat tres rectangles. En el primer, la llargada mesura 3 cm més que l'amplada. El segon i tercer rectangle tenen unes dimensions augmentades, respectivament, en 1 cm i 2 cm respecte de les dimensions del primer. Si la suma dels tres perímetres és de 162 cm, quines són les dimensions de cada rectangle?

Answers

Resposta:

Primer rectangle:

Amplada = 11

Longitud = 14

Segon rectangle:

Amplada = 12

Longitud = 15

Tercer rectangle:

Amplada = 13

Longitud = 16

Explicació pas a pas:

Donat que:

Primer rectangle:

Amplada = x

Longitud = x + 3

2n rectangle:

Augment de la dimensió d'1 cm respecte al primer rectangle;

Amplada = x + 1

Longitud = x + 4

3r rectangle:

Augment de la dimensió de 2 cm respecte al primer rectangle;

Amplada = x + 2

Longitud = x + 5

Suma dels tres perímetres del rectangle:

Perímetre d'un rectangle: 2 (l + O)

Primer rectangle:

2 (x + x + 3) = 2 (2x + 3) = 4x + 6

2n:

2 (x + 1 + x + 4) = 2 (2x + 5) = 4x + 10

3r:

2 (x + 2 + x + 5) = 2 (2x + 7) = 4x + 14

Suma de perímetres = 162

(4x + 6 + 4x + 10 + 4x + 14) = 162

12x + 30 = 162

12x = 162 - 30

12x = 130

x = 11

Per tant,

Primer rectangle:

Amplada = 11

Longitud = 11 + 3 = 14

2n rectangle:

Amplada = 11 + 1 = 12

Longitud = 11 + 4 = 15

3r rectangle:

Amplada = 11 + 2 = 13

Longitud = 11 + 5 = 16

How do I plot this?


Answers

you should have a dot on the -2 on the y line

HELP only answer to give right answer pleaseeee

Answers

Answer:

B=4

Step-by-step explanation:

The Y intercept is where the line meets with the middle of the graph

B=4!!!
The y-intercept of the line is B4

really confused on this! help is appreciated!!

Answers

I am not sure what the question is asking but that line’s slope is 3/2 and the point (1,4) is on the line so the first line on the table is correct for that graph

the temperature at noon at an Antarctic weather center was –15 °C. At midnight it had fallen by 12 °C. What was the temperature at midnight?

Answers

Answer:

-27 °C

Step-by-step explanation:

-15 -12 = -27

Bella makes bracelets. She uses 20 beads for each bracelet. How
many beads will she use to make 7 bracelets?

Answers

Answer:

140 beads.

Step-by-step explanation:

Hope this helps. :)

Given a+2 when a=5 I need help

Answers

Answer:

The answer to this is 7.

a+2

5+2

7

The answer would be 7 so the top person is right :)

Read the top and answer the question!!

Answers

Answer:

Um... ithink it would be 3 but please tell me and correct me if im wrong

Step-by-step explanation:

A car dealership sold 84 cars in April. The dealership wants to increase the number of cars sold by 25% in May. How many cars will the dealership need to sell to reach their goal?

Answers

Answer: 105 Cars

Step-by-step explanation: To get an increase of 25% you need to multiply 84 by .25 then add the product of that to 84 to get 105

The number of cars dealership need to sell to reach their goal is, 105 cars

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

A car dealership sold 84 cars in April,

The dealership wants to increase the number of cars sold by 25% in May

The number of cars dealership need to sell to reach their goal = ?

This represents a 25% increase, which is the same as adding one quarter to the original number of cars sold.

The car dealership wants to increase the number of cars sold by 25% in May, which means that they want to sell,

⇒ 84 x 1.25 = 105 cars

So, the dealership will need to sell 105 cars in May in order to reach their goal of increasing the number of cars sold by 25%.

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HELPPPPPPPP T^T I NEED AN ANSWER!!!! IS THE QUESATIN A OR C

Answers

Answer:

Commutative

Please, mark as brainliest

9(p-4)=-189(p−4)=−18

Answers

Answer:

6

Step-by-step explanation:

Answer:

The Correct Answer is 2

Step-by-step explanation:

Trust me for I have the skills of a scientist

Explain why 186,426 Is diviable by both 3 and 9

Answers

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A number is divisible by 9 if the sum of its digits is divisible by 9.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{9} = \frac{27}{9} = 3 \\ [/tex]

Thus 186,426 is divisible by 9 .

_________________________________

Also a number is divisible by 3 if the sum of its digits is divisible by 3.

Look :

[tex] \frac{1 + 8 + 6 + 4 + 2 + 6}{3} = \frac{27}{3} = 9 \\ [/tex]

Thus 186,426 is divisible by 3 .

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Two airplanes are carrying food and medical supplies to a country in needOne airplane is carrying 63 meals and 51 medical The total the supplies on that airplane is The other airplane is carrying 77 meals and 51 medical kitsThe cost for the supplies on that airplane Write and solve a system of equations to find the price of one meal and the price of one third airplane is carrying 70 meals and 62 medical , what is the total cost of supplies

Answers

Answer:374

Step-by-step explanation:

you add them all then get the total

helpp

2^2 - (2)(-2) - (-2)^2​

Answers

Answer:

4

Step-by-step explanation:

2^2 - (2)(-2) - (-2)^2

=4+4-4

=4

2² - (2 × -2) - (-2²)

= 4 - (-4) - 4

= 4 + 4 - 4

= 8 - 4

= 4

b) How far does the car travel in 4 hours?

Answers

Answer:

70 miles per hour

Step-by-step explanation:

Answer:

A car can travel up to 240 km in 4 hours.

Step-by-step explanation:

A car travels 60 MPH meaning 60(miles) times 4(hours) is 240.

Find the centroid of the triangle with these vertices: P (-1,7), Q (9,5), and R (4,3).
The coordinates of the centroid are?​

Answers

Answer:

The coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

Step-by-step explanation:

Given the vertices

P (-1, 7)Q (9, 5)R (4, 3)

We know that the intersection of medians brings the centroid of the triangle.

The centroid of a triangle is given by

[tex]O\:=\:\left(\frac{P_x+Q_x+R_x}{3},\:\frac{P_y+Q_y+R_y}{3}\:\right)[/tex]

In this example,

[tex]P_x=-1,\:P_y=7[/tex]

[tex]Qx=9,\:Q_y=5[/tex]

[tex]Rx=4,\:R_y=3[/tex]

substituting in the formula

[tex]O\:=\:\left(\frac{-1+9+4}{3},\:\frac{7+5+3}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(\frac{12}{3},\:\frac{15}{3}\:\right)\:\:[/tex]

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

Therefore, the coordinates of the centroid are:

[tex]O\:=\:\left(4,\:5\right)\:\:[/tex]

The diagram is also attached below.

We've been given with the co-ordinates of vertices of the triangle and asked to calculate the co-ordinates of the centroid.

Centroid of a triangle :-

[tex]\red{\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} } \: , \: \dfrac{y_1 \: + \: y_2 \: + \: y_3}{3} }} \: \pink\bigstar [/tex]

We have :

x₁ = -1x₂ = 9x3 = 4y₁ = 7y₂ = 5y3 = 3

Substituting the values :

For x co-ordinate:-

[tex]: \: \implies \: \sf{x\: = \: \dfrac{x_{1} \: + \: x_2 \: + \: x_3}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ - 1 \: + \: 9 \: + \: 4}{3}} \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 8 \: + \: 4}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: \cancel\dfrac{ 12}{3} } \\ \\ : \: \implies \: \sf{x\: = \: 4 }[/tex]

For y co-ordinate:-

[tex]: \: \implies \: \sf{y\: = \: \dfrac{y_{1} \: + \: y_2 \: + \: y_3}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 7 + 5 + 3}{3}} \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 10 \: + \: 5}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: \cancel\dfrac{ 15}{3} } \\ \\ : \: \implies \: \sf{y\: = \: 5 }[/tex]

Henceforth,

Co-ordinates are (4 , 5)

Additional Information :

Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

Distance Formula :-

[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]

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бx +7= 8х - 15
Pls help will mark brainliest

Answers

Answer:

X=11

Step-by-step explanation:

-6x both sides of = sign

+ 15 both sides of = sign

x=11

helpppp
i need help quickly

Answers

Answer: 140?

I am not really sure but I think 140......

The answer is ————- 70

Wykonaj mnożenie i zredukuj wyrazy podobne (x+5)(x+4)(x+3).

Answers

Answer:

.........................

Slove the sum
-15 > - 16 + y

Answers

Answer:

Let's solve your inequality step-by-step.

−15>−16+y

Step 1: Simplify both sides of the inequality.

−15>y−16

Step 2: Flip the equation.

y−16<−15

Step 3: Add 16 to both sides.

y−16+16<−15+16

y<1

Answer:

y<1

please help i’ll give brainlest and lots of points !!

Answers

you should repost i’ll try and answer then

HELP MEEEE PLEASE i don't know how to do this

Answers

Answer:

5 hours

Step-by-step explanation:

35x+25 = 40x

25=5x

x= hours

I NEED HELP ASAP IT IS FOR CHRISTMAS!!!!!!THESE ARE ALL MY POINTS!!
If three kids that want to buy something that cost $35.99 how much would each of them have to pay? Any ideas for what i should get my mom and dad?!!!! please help

Answers

Answer:

They should pay $12 each

Answer:

about 12 dollars probably more with tax maybe around 12.03

please help i’ll give brainliest!!

Answers

Answer:

no correlation

Step-by-step explanation:

the dots are all scattered randomly

For a dinner party, a catering company charges a set
fee of $150 plus $20 per person.
How much will it cost for 35 people to attend the event?
Justify your work

Answers

Answer:

$850

Step-by-step explanation:

35 x 20 = 700 + 150 = $850 or 850

$20 per person and 35 people = $700 + the $150 fee = $850

how many times does 90 go into 490

Answers

Answer:

may be 5 times is answer but I am not sure I have done 5 times I got like this

Liberty Middle School’s enrollment increased to 660 students. This is an increase of 10% over last year’s enrollment. What was last year’s enrollment?

Answers

Answer:

600

Step-by-step explanation:

Last years enrollment was 100% of the number.

This year, the enrollment went up by 10%, so now, it's 110% of last years number.

Let last year's enrollment be x.

110% of x is 660

1.1x = 660

x = 660/1.1

x = 600

Answer: 600

Answer:

600

Step-by-step explanation:

You have a standard deck of cards. What is the probability of drawing a heart or a face card?

Answers

Answer:

3/4

Step-by-step explanation:

What is the surface area of the solid?

Answers

Answer:

B

Step-by-step explanation:

What would 3 1/3 be if you had to borrow?

Answers

we will eat chocolate of rupee 1 and divide other amount ofoney equally

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