Extra Credit:
8 congruent spheres are packed into a cube with
edge length x so that each sphere is tangent to 3
faces of the cube and 3 other spheres as shown.
what is the ratio of the total volume of the
spheres of the volume of the cube?

Extra Credit:8 Congruent Spheres Are Packed Into A Cube Withedge Length X So That Each Sphere Is Tangent

Answers

Answer 1

Answer:

Ratio of the volumes of the spheres and cube = 0.523

Step-by-step explanation:

From the figure attached,

Diameter of one sphere = Half of the measure of one side of the cube

                                        = [tex]\frac{x}{2}[/tex]

Radius of the sphere = [tex]\frac{\frac{x}{2}}{2}[/tex]

                                   = [tex]\frac{x}{4}[/tex]

Volume of a cube is given by the formula,

V = [tex]\frac{4}{3}\pi r^{3}[/tex]

Therefore, volume of one sphere = [tex]\frac{4}{3}\pi (\frac{x}{4})^{3}[/tex]

                                                        = [tex]\frac{x^3\pi}{48}[/tex]

Volume of 8 spheres = [tex]8\times \frac{x^3\pi}{48}[/tex]

                                   = [tex]\frac{x^3\pi}{6}[/tex]

Volume of a cube = (side)³

                              = [tex]x^3[/tex]

Ratio of the volumes of the sphere and cube = [tex]\frac{\frac{\pi x^3}{6} }{x^3}[/tex]

                                                                              = [tex]\frac{\pi}{6}[/tex]

                                                                              ≈ 0.523

Extra Credit:8 Congruent Spheres Are Packed Into A Cube Withedge Length X So That Each Sphere Is Tangent

Related Questions

HELP PLEASE
ILL MARK BRAINLIEST

Answers

Answer:

2.3

Step-by-step explanation:

did the math

So, basically the x is 2.3 !

El espesor de un borde de un componente de una aeronave está distribuido de manera uniforme entre 0.05 y 1.05 milimetros.Obtenga la función de distribución acumulada del espesor del borde.Calcule la proporción de bordes cuyo espesor es mayor que 1.02 milimetros.Qué espesor estEa excedido por el 90% de los bordes.Calcule la media y la varianza del espesor.

Answers

Answer:

a) [tex]F(x)\begin{cases} & 0\text{ if } x \leq 0.05 \\ \\ &\dfrac{x - 0.05}{1.05 - 0.05} = x - 0.05 \text{ if } 0.05 \leq x \leq 1.05 \\ \\ & 1 \text{ if } x \geq 1.05 \end{cases}[/tex]

b) 0.03

c) 0.15

d) La media es 0.55

La varianza es 8.[tex]\overline 3[/tex]

Step-by-step explanation:

La variación del espesor del componente de la aeronave = 0.05 a 1.05

El pdf de la variable 'X' se da de la siguiente manera;

[tex]f(x) = \dfrac{1}{1.05 - 0.05} = 1[/tex] por 0.05 < x < 1.05

a)

[tex]F(x)\begin{cases} & 0\text{ si } x \leq 0.05 \\ \\ &\dfrac{x - 0.05}{1.05 - 0.05} = x - 0.05 \text{ si } 0.05 \leq x \leq 1.05 \\ \\ & 1 \text{ si } x \geq 1.05 \end{cases}[/tex]

b) Para la proporción de los bordes que con un espesor superior a 1.02 milímetros, obtenemos;

P(X > 1.02) = 1 - F(1.02) = 1 - (1.02 - 0.05) = 0.03

P(X > 1.02) = 0.03

La proporción de bordes que tienen un espesor mayor que 1.02 = 0.03

c) El espesor, 'x', excedido en el 90% de los bordes, se encuentra de la siguiente manera;

P(X > x) = 1 - F(x)

∴ 90/100 = 0.9 = 1 - F(x) = 1 - (x - 0.05)

x - 0.05 = 1 - 0.9 = 0.1

x = 0.1 + 0.05 = 0.15

∴ El espesor excedido en el 90% de los bordes, x = 0.15

d) Para una variable aleatoria uniforme continua, a ≤ x ≤ b, tenemos;

[tex]El \ significado, \mu = E(X) = \dfrac{(a + b)}{2}[/tex]

[tex]La \ varianza, \sigma^2 = V(X) = \dfrac{(b - a)^2}{12}[/tex]

Para la distribución de espesor de borde dada, tenemos;

0.05 < x < 1.05

[tex]\therefore El \ significado, \mu = E(X) = \dfrac{(0.05 + 1.05)}{2} = 0.55[/tex]

El significado E(X) = 0.55

[tex]La \ varianza, \sigma^2 = V(X) = \dfrac{(1.05 - 0.05)^2}{12} = 1/12 = 8.\overline 3[/tex]

La varianza, V(X) = 8.[tex]\overline 3[/tex]

Identify the volume and surface area of the sphere in terms of π.

The figure shows a sphere. The sphere has a radius of 9 centimeters.

V = 972π cm3; S = 324π cm2
V = 243π cm3; S = 324π cm2
V = 972π cm3; S = 162π cm2
V = 243π cm3; S = 162π cm2

Answers

Answer:

Volume is: 972 and Surface area is 324

Step-by-step explanation:

How to get the volume is 9^3

That is 729

Times 4/3

972.

The surface area is 4 times 9^2

324.

You dont use the pie.

Which of the following are not equivalent? *

1/3 and 5/15
1/4 and 0.25
0.6 and 6%
1/2 and 50%

Best answer get brainliest. 5 stars and a heart

Answers

1/3 and 5/15 that’s the answer
0.6 and 6% are not equivalent.

To turn a decimal into a percentage you move the decimal place two places to the right. By doing this you can see that 0.6 = 60% and is not equivalent to 6%. I hope this helps!

Please help me this is my end of the year work

Answers

Answer:

Triangle, pentagon, heptagon, and decagon.

Step-by-step explanation:

REMEMBER THIS:

DECAGON: 10 SIDES

HEPTAGON: 7 SIDES

PENTAGON: 5 SIDES

TRIANGLE: 3 SIDES

EXTRA INFO:

HEXAGON: 6 SIDES

QUADRILATERAL: 4 SIDES

OCTAGON: 8 SIDES

NONAGON: 9 SIDES

solve for p
p+23.7=41.13

Answers

Answer:

p=17.43

Step-by-step explanation:

To solve this I just subtracted

p=41.13-23.7

which is

p=17.43

Someone please help me

Answers

Answer:

y=x^2 - 1, y=5x^3 + 9, and y=2x(x-3)

Step-by-step explanation:

these equations are either parabolas or a cubic function. These graphs do not have a constant rate of change, proving that Jimmy is incorrect. y=20-4x and y=15 are both straight lines/linear.

Please Help me with this question!! I have a time limit

The Garcia family drives 3/4 of the distance to their grandparent's house
in 3/4 hour.

How many hours will it take
to drive to their grandparent's house at the same rate?

a= 1
b=9/16
c=1 and 7/9

Answers

Answer:

a=1

Step-by-step explanation:

because 3/4 hour is 45 minute and it takes 4/4 distance to their grandparents hous ein 4/4 hour so 45÷3=15, 15×4=60 which is 1hour

The Answer is A: 1 hour

Step-by-step explanation:

since they can drive 3/4 the distance in 3/4 hours, they can also drive 1/2 the distance in 1/2 hours and so on. If they want to visit the grandparent's house, they need to drive 4/4 the distance which is equivalent to 1 so it will take 1 hour for them to go to the house at the same rate.

A Tip From Me To You:

sometimes the question tries to trick you to make you overthink it so don't overthink it, try to just solve it simply.

Have a great day! <3

HeLP PLEASE OH LORD ITS TIMED 20 POINTS AM I RIGHT??? IF NOT WHATS THE ANSWER

Answers

Answer:

you are correct :D

Step-by-step explanation:

Mallory decided to keep track of how long she watched TV for an entire week. She watched 1 hour and 25 minutes of comedy shows, 45
minutes of drama shows, and 3 hours of action shows.
What was the ratio of number of minutes she watched comedy shows to the total number of minutes she watched TV.
A. 17:36
B. 17:45
C. 17: 60
D. 17 : 62

Answers

Answer A answer A answer A

PLEASE HELP! I HAVE MY STAAR TEST TOMORROW!!!!

Answers

Answer:

152

Step-by-step explanation:

blue -- 8 x 2 = 16 x 2 = 32

green -- 8 x 6 = 48 x 2 = 96

red -- 6 x 2 = 12 x 2 = 24

96 + 24 + 32 = 152

What is the volume of the rectangular prism - i ready. 1/3 ft some of. The answers 1 1/9 feet3- 10 ft3 - 2/9 ft3 - 3 1/3 ft3

Answers

Answer:

[tex]3\frac{1}{3}\ ft^3[/tex]

Step-by-step explanation:

A rectangular prism is a polyhedron with six rectangular faces. The volume of a prism is given by:

Volume = width * height * length

From the diagram, the rectangular prism is made up of cubes. Each cube is has a size of 1/3 ft by 1/3 ft.

The height of the prism is made up of 5 cubes. Height = 5 * 1/3 = 5/3 ft.

The length of the prism is made up of 3 cubes. length = 3 * 1/3 = 1 ft.

The width of the prism is made up of 2 cubes. Width = 2 * 1/3 = 2/3 ft.

The volume of the prism = width * height * length = 2/3 * 5/3 * 1 = 10/9 ft³ =  [tex]3\frac{1}{3}\ ft^3[/tex]

Answer:

it is 3 1/3 good day

Step-by-step explanation:

find the volume of the cylinder

Answers

Step-by-step explanation:

8 volume

10x+24y=200
y=x+3
Pleas help me

Answers

Answer:

The answer should be x=3.76

Step-by-step explanation:

Someone plz help me I suck at doing that

Answers

Answer:

D - 4.6

Step-by-step explanation:

Hope it Helps!

:)

and sorry for the late answer

A cube with a surface area of 150 square centimeters is shown. Eight cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters, of the new larger cube?​

Answers

Answer:

1000 cubic centimeters

Step-by-step explanation:

150 / 6 = 25

Square root of 25 = 5

5 * 2 = 10

10 * 10 * 10 = 1000 cubic centimeters

A bag contains 5 blue marbles, 8 green marbles, and 11 red marbles. What is the probability of choosing a purple marble?
A. .208
B. .458
C. .667
D. 0

Answers

Answer:

0

Step-by-step explanation:

the bag has nothing purple marbles

I need some help I will give you brainiest.
A teaspoon of common table salt contains about 2,000 mg of sodium. How many grams of sodium is this?

200 g

2 g

2,000,000 g

20 g

Answers

2 grams because 1000 milligrams = 1 gram

$27 for 4 large pizzas or $32 for 5 large pizzas​

Answers

Answer: 5 large

Step-by-step explanation:

$6.75 per pizza for 4 large pizzas

$6.40 per pizza for 5 large pizzas

I really need help! it’s due soon:)

Answers

Answer:

(5, 5), (7, 2), (3, 2)

Step-by-step explanation:

When reflecting a figure across the y-axis, the x value will be the opposite and the y value will remain the same

reflection across y-axis:

(x, y) ---> (-x, y)

Hope this helps!!

Question 7

Which set of side lengths can be used to form a right

triangle?

Answers

Answer:

D.30,40,50

Step-by-step explanation:

A.4,5,6

B.2,3,4

C.10,20,30

D.30,40,50

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

4² + 5² = 25 is not equal to the square of 6 which is 36

2² + 3² = 10 . 10  is not equal to the square of 4 which is 16

10² + 20³ = 500. 500  is not equal to the square of 30 which is 900

30² + 40² = 2500. this is equal to the square of 50

(2) Find the area of each circle to the nearest tenth

Pls show the work not just give me the answer

Answers

Answer:

38.5 mm^2

Have a nice day!

Step-by-step explanation:

Area = πr^2

Area = π(3.5^2)

Area = π(12.25)

Area = 38.48451...

Area = 38.5

Evaluate t-⅓=8 no like please and thanks​

Answers

Answer:

If its t to the power - 1/3 then it is 1/512

Step-by-step explanation:

t^-1/3=8

(1/t) ^1/3 =8

1/t = 8 ^3

t=1/512

please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

The right answer is

tan D =80/18

I want to d!e ahahahahahaha

Answers

Answer:

dont say that-

Step-by-step explanation:

Kari lost 2.88 kilograms after two weeks of exercise. One kilogram is equal to approximately 2.2 pounds. Which measurement is closest to the number of pounds that Kari lost? Group of answer choices

Answers

Answer:

Amount of weight Kari lost in pound = 6.34 pound (Approx.)

Step-by-step explanation:

Given;

Amount of weight Kari lost in kilogram = 2.88 kilograms

Given scale;

1 kilogram = 2.2 pound

Find:

Amount of weight Kari lost in pound

Computation;

Amount of weight Kari lost in pound = Amount of weight Kari lost in kilogram x  2.2 pound

Amount of weight Kari lost in pound = 2.88 x 2.2 pound

Amount of weight Kari lost in pound = 6.336

Amount of weight Kari lost in pound = 6.34 pound (Approx.)

5/1(x-2)=1/10(x+6). hep me guys pls i don't undestant math

Answers

Answer:

[tex]x=\frac{106}{49}[/tex]

Step-by-step explanation:

Therefore, [tex]x=\frac{106}{49}[/tex] will be your final answer.

Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. How much fabric will he need?

A square pyramid with a base of 4 meters by 4 meters and triangular side heights of 3 meters.

16 meters squared
24 meters squared
36 meters squared
40 meters squared
ITS NOT 24

Answers

The amount of fabric Henri will need is 40 meters squared

The amount of fabric Henri will require is the surface area of the square pyramid.

What is the surface area of the square spyramid?

The surface area of the square pyramid, A = area of square base, A' + area of 4 triangular sides

Area of square base

The area of the square base is A' = L² where L = length of base = 4 m

So, A = L²

= (4 m)²

= 16 m²

Area of triangular side

The area of the triangular side is A" = 1/2Lh where

L = length of base = 4 m and h = height of triangle = 3 m

So, A" = 1/2Lh

= 1/2 × 4 m × 3 m

= 1/2 × 12 m²

= 6 m²

Since there are 4 triangular sides, the area of the sides of the pyramid is

4A" = 4 × 6 m²

= 24 m²

Amount of fabric Henri will need

Since the amount of fabric Henri will need is the surface area of the square pyramid,

So, The surface area of the square pyramid, A = A' + 4A"

= 16 m² + 24 m²

= 40 m²

So, the amount of fabric Henri will need is 40 meters squared

Learn more about surface area of square pyramid here:

https://brainly.com/question/22744289

#SPJ1

The equation of the trend line is y = -0.36x + 12.6 use the equation to of the trend line to predict the wind chill for a wind speed of 51 mi/h round your answer to the nearest degree. The wind chill at 51 mi/h

Answers

Given:

The equation of the trend line is:

[tex]y=-0.36x+12.6[/tex]

In this equation y represents the wind chill and x represents the wind speed.

To find:

The wind chill at 51 mi/h.

Solution:

We have,

[tex]y=-0.36x+12.6[/tex]

Putting [tex]x=51[/tex], we get

[tex]y=-0.36(51)+12.6[/tex]

[tex]y=-18.36+12.6[/tex]

[tex]y=-5.76[/tex]

Round the answer to the nearest degree.

[tex]y\approx -6^\circ[/tex]

Therefore, the wind chill at wind speed 51 mi/h is -6°.

please help me with 7 and 8. If they’re right i’ll give you brainliest.

Answers

Answer:

7,D all real numbers greater than or equal to 0

8,G all real numbers less than or equal to 2

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