A glass ball is packed in the box shown. Which expression represents the volume of foam padding needed to fill the space in the box around the sphere in terms of Pi

A Glass Ball Is Packed In The Box Shown. Which Expression Represents The Volume Of Foam Padding Needed
A Glass Ball Is Packed In The Box Shown. Which Expression Represents The Volume Of Foam Padding Needed

Answers

Answer 1

Answer: (27- 4/3 pi) r^3

Step-by-step explanation: 1. Volume of a cube: V= a^3,  V= 3^3 , V=27

2.  Volume of a sphere: V=4/3 pi r^3 ......

Answer 2

The expression which represents the volume of the foam padding needed to fill the space in the box around the sphere in terms of π is option C. (27 - [tex]\frac{4}{3}[/tex] π) r³.

What is Volume?

Volume of a three dimensional shape is the space occupied by the shape.

We have a sphere of radius r inside a cube of side length 3r.

Volume of a cube = (a)³, where a is the side length.

Here a = 3r

Volume of the cube = (3r)³ = 27r³

Volume of a sphere of radius r = [tex]\frac{4}{3}[/tex] π r³

Volume of the foam padding needed to fill the space in the box around the sphere = 27r³ - [tex]\frac{4}{3}[/tex] π r³

                  = r³ (27 -  [tex]\frac{4}{3}[/tex] π)

Hence the volume of the space inside the cube outside the sphere is r³ (27 -  [tex]\frac{4}{3}[/tex] π).

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Related Questions

The image of a triangle after it has been dilated with a center of dilation at the origin has vertices at A prime(12, –6), B prime(–24, –12), and C prime. If the pre-image of B prime, point B, has coordinates of (–18, –9) and the pre-image of C prime, point C, has coordinates of (–13.5, 18), which statements are true? Check all that apply. The coordinates of C prime are (27, 18). The coordinates of C prime are (–18, 24). The scale factor is 1 and one-third. The scale factor is 1 and one-fifth. The scale factor is Three-fourths. The coordinates of A are (16, –8). The coordinates of A are (9, –4.5).

Answers

Answer:

C is (-18, 24)

Scale factor --> 1 1/3

A is (9, - 4 1/2)  *4 1/2 is also 4.5

Brainliest please, I need a few more :D

The true statement are; The coordinates of C prime are (–18, 24). The scale factor is 1 1/3 . The coordinates of A are (9, –4.5).

How to find if a pair of figure is not dilated version of each other?

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.

At image B (-24, -12) and pre image B (-18, -9),

we can work out the scale factor by (-24/-18) and (-12/-9) both equal 4/3

Using the scale factor to go from the pre image to the image,

We can find C coordinate by pre image C by the scale factor.

C is (-13.5 x 4/3) and (18 x 4/3)

C is (-18, 24)

So, The scale factor is 4/3, which is the mixed numeral of 1 1/3.

To find the pre image of point A;

A is (12/(4/3)) and (-6/(4/3))

A is (9, - 4 1/2)

Hence, the true statement are;

The coordinates of C prime are (–18, 24).

The scale factor is 1 1/3 .

The coordinates of A are (9, –4.5).

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Which of the following could be the equation of the line passing through (8, 3) parallel to y = -2.
y = 8
x = 8
y = 3
x = 3

Answers

y = 3. y=-2 and y=3 have the same slope, so they are parallel. y=3 also passes through the point (8,3).

The base of a rectangular prism has an area of 19.4 square meters and the prism has a volume of 306.52 cubic meters. Write an equation that can be used to find the height h of the prism. Then find the height of the prism.

Answers

Answer:

15.8

Step-by-step explanation:

The formula would be V = Bh, the Base being LxW.

Since we already know the base and volume, we can substitute it into the formula.

306.52 = 19.4(h). Divide by 19.4, and you get 15.8 as your answer.

Hope that helps! Tell me if im worng, im only a student .m.

Stewart purchased 15/20 gallons of juice for his party. Guests drank 9/20 gallons, so how much juice is left?

Answers

Answer:

Step-by-step explanation:

6/20 Gallons

Answer:

[tex]\frac{3}{10}[/tex].

Step-by-step explanation:

To do this, we will need to subtract fractions.

[tex]\frac{15}{20}-\frac{9}{20}=\frac{6}{20} =\frac{3}{10}[/tex] (Simplified)

Please help!! Thanks!

Answers

Answer:

C

Step-by-step explanation:

A Bowling ball is rolled down the alley with the constant velocity of 1.6 m/sec at an angle of 85° to the starting line, the position of the person throwing a bowling ball can be represented by the point (0,0). where is the ball after six seconds?

Answers

We have been given that a Bowling ball is rolled down the alley with the constant velocity of 1.6 m/sec at an angle of 85° to the starting line, the position of the person throwing a bowling ball can be represented by the point (0,0).

We are asked to find the position of ball after 6 seconds.

We will use horizontal position and vertical position formula to solve our given problem.

Horizontal position is given by formula: [tex]x=v\cdot \text{cos}(\theta)\cdot t[/tex] and vertical position is given by formula: [tex]y=v\cdot \text{sin}(\theta)\cdot t[/tex],where,

v = Velocity,

t = Time,

[tex]\theta[/tex] = Angle to the starting line.

For our given problem [tex]v=1.6[/tex], [tex]t=6[/tex] and [tex]\theta=85^{\circ}[/tex].

[tex]x=1.8\cdot \text{cos}(85^{\circ})\cdot 6[/tex]

[tex]x=10.8 \cdot 0.087155742748[/tex]

[tex]x=0.9412820216784\approx 0.94[/tex]

[tex]y=1.8\cdot \text{sin}(85^{\circ})\cdot 6[/tex]

[tex]y=10.8\cdot 0.996194698092[/tex]

[tex]y=10.7589027\approx 10.76[/tex]

Therefore, the position of ball after 6 seconds would be [tex](0.94,10.76)[/tex].

Answer:

(0.8,9.6)

Step-by-step explanation:

x=1.6*cos85* 6=0.8

y=1.6*sin85 *6=9.6

please help!!!! thank you

Answers

Answer:

9 c^7

Step-by-step explanation:

Answer:

27c^2-4

Step-by-step explanation:

27c to the 2nd power minus 4

Evaluate 3a + b to the second power if a=2 and b=3
PS : can you help me with 1, 2 and 3 ?!

Answers

Answer:

1. 3

2. 3

3. 15

Step-by-step explanation:

Please help ASAP will mark brainliest

Answers

the points are (1,8) :)

Which expression is equivalent to 10√5

Answers

Answer:

A. √500

Step-by-step explanation:

Since 500 = 5·100 = 5·10² you can move the 10² out of the √ as 10.

Hence 10√5 = √500

So we're using these rules:

√a·b = √a·√b

and of course

√a² = a  (a>0)

Simplify the expression below. (3^5)^3


3^3

3^5

3^8

3^15

Answers

Answer:

14348907

Step-by-step explanation:

3^15 is it put in scientific notation.

Answer:

14348907

Step-by-step explanation:

Joe has 10 marbles. Ken has fewer marbles than Joe. Which inequality represents the
number of marbles m that Ken has?
m
= 10
m
<10
m
> 10
m
< 10

Answers

Answer:

The 2nd and 4th (m<10)

Step-by-step explanation:

The symbol used is a less than sign, so the inequality is saying m is less than 10, and since Ken=m Ken has fewer marbles.

Answer:

Step-by-step explanation:

Chad's bedroom floor is 19 feet long and 19 feet wide. He has an area rug on his floor that is 5 feet long and 8 feet wide.

Which statement tells how to find the amount of the floor that is not covered by the rug? Select all that apply.

A Add 19 + 19 + 5 + 8.
B Subtract 40 from 19 × 19.
C Subtract 19 × 8 from 19 × 5.
D Add 19 × 19 and 5 × 8.
E Subtract 5 × 8 from 19 × 19.
F Subtract 19 × 19 from 5 × 8.

Answers

Answer:

B and E

Step-by-step explanation:

Subtract the area of the rug from the bedroom floor.

Answer:

E

Step-by-step explanation:

Area of the floor that is not covered = Area of floor - area of rug

= 19 *19 - 5*8

= 361 - 40

= 321 Sq.ft

The data below shows the scores of some students on a test: 21, 27, 29, 20, 22, 33, 23 Which box plot represents the data?

Answers

Answer:

23

Step-by-step explanation:

you take the greatest and least greatest number until only one is left.

21, 27, 29, 20, 22, 33, 23

21, 27, 29, 20, 22, 23

21, 27, 29, 22, 23

27, 29, 22, 23

27, 23

23

-10-9-8-7-6-5-4-3-2
-1 0
1
2
3
4 5 6 7 8 9 10
Determine the distance between -1 and -7.
-1
A)
-8 units
B)
-6 units
C)
6 units
D)
8 units

Answers

Answer:

B)6 units

Step-by-step explanation:

-10-9-8-7-6-5-4-3-2-1 01234 5 6 7 8 9 10

or

-7-(-1)=-6

Distance can't be a negative so the answer is 6.

Kim is packing eggs into boxes. Each box holds 6 eggs. She has 94 eggs. What is the smallest number of boxes she needs to pack all the eggs?

A. 15.65
B. 15.67
C. 15.7
D. 16

Answers

Answer:

D

Step-by-step explanation:

For this one (and others that are similar to this one) you can't have a portion of a box, therefore, you can eliminate all the other answers.

The smallest number of boxes she needs to pack all the eggs is 15.67,

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total Eggs = 94

Each box Hold= 6 eggs

So, number of boxes required to hold 94 eggs

= 94 / 6

= 15.66

Hence, smallest number of boxes she needs is 15.67

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Evaluate tan²0 for 0 = 60°.
1/3
3/4
1
3

Answers

Answer:

3

Step-by-step explanation:

i Substituted the value ofthe variable into the equation and simplified it.

HELLPPPPPP
S S DS ADS


A

Answers

Answer:

90%

Step-by-step explanation:

9/10 = 90/100

the answer to the equation is 90

what is the center?
the circle passes through the point (-7,-7). what is the radius?​

Answers

We have been given image of circle that passes through point [tex](-7,-7)[/tex]. We are asked to find the radius of the circle.

First of all, we will find the center of the circle.

We can see that center of circle is at point [tex](-2,-1)[/tex].

Now we will use equation of circle to find radius.

[tex](x-h)^2+(y-k)^2=r^2[/tex], where, point (h,k) represents center of circle and r represents radius of circle.

Now we will substitute the coordinates of point [tex](-7,-7)[/tex] and coordinates of center [tex](-2,-1)[/tex] and solve for r as:

[tex](-7+2)^2+(-7+1)^2=r^2[/tex]

[tex](-5)^2+(-6)^2=r^2[/tex]

[tex]25+36=r^2[/tex]

[tex]61=r^2[/tex]

Switch sides:

[tex]r^2=61[/tex]

Now we will take positive square root on both sides:

[tex]\sqrt{r^2}=\sqrt{61}[/tex]

[tex]r=\sqrt{61}[/tex]

Therefore, radius of circle will be [tex]\sqrt{61}[/tex] and center is at point [tex](-2,-1)[/tex].

What’s the answer????

Answers

Answer:

80

Step-by-step explanation:

the formula is base times height the height is 10 and the base is 8 so 10 times 8 equals 80

I believe ur answer is 80 :)

What is the probability of spinning a 2 both times?

Answers

Answer:

the posbilities is an hour

Step-by-step explanation:

30  + 30 mins = 1 hour

URGENT WILL MAKE BRAINLEST
Each month, Daniel budgets $1230 for fixed expenses, $780 for living expenses, and $160 for
annual expenses. His annual net income is $30,300.
Which statement best describes his monthly budget?
It shows a deficit of $355
It shows a surplus of $355.
It shows a surplus of $515.
It is balanced.

Answers

Answer:

B

Step-by-step explanation:

Monthly net income = 30300/12 = $2525

Total monthly expenses = 1230+780+160 = $2170

Surplus = 2525 - 2170 = $355

The value of the cash flow will be $355 which is surplus. Then the correct option is B.

What is cash flow?

The cash balance of liquid assets coming into and going out of a business is referred to as cash flow. Money spent and money received reflect inflows and outflows, respectively.

The cash flow is the difference between outflow and inflow.

Cash flow = outflow - inflow

If the value of the cash flow is negative that means the expense is more.

If the value of the cash flow is positive that means the income is more.

Every month, Daniel spending plans $1230 for fixed costs, $780 for everyday costs, and $160 for yearly costs. His yearly overall gain is $30,300.

Then the Cash flow is calculated as,

Cash flow = ($30,300 / 12) - ($1,230 + $780 + $160)

Cash flow = $2,525 - $2,170

Cash flow = $355

The value of the cash flow will be $355 which is surplus. Then the correct option is B.

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Classify the following triangle. Check all that apply.
51
12.1
/59
70"
10
A. Scalene
I B. Equilateral
O C. Right
D. Acute
O E. Obtuse
O F. Isosceles

none of the answers I saw had the same triangle ​

Answers

Answer:

acute

Step-by-step explanation:

the largest number for the angles is 70 wich is an acute number and since the angles are all not equal its not equilateral

Answer:

it D . acute and A .scalene

math question down below

Answers

Answer:

560 is the area

Step-by-step explanation:

20x10 = 200 + the 30x12 = 560 comment if you need further explanation

Find the length of DF

Answers

Answer:

7x-58

just add all the terms

3x-28+3x-30+x
7x-58 =33
7x=91
X=13
Soooo df= 6x-58
6*13-58=20
20 is the correct answer

please help, I dont know how to do this​

Answers

Answer:

[tex]\frac{y-2}{4}[/tex]

Step-by-step explanation:

Let's start by factoring everything:

[tex]\dfrac{\frac{y^2+y}{y^2-2y}}{\frac{4y+4}{y^2-4y+4}}=[/tex]

[tex]\dfrac{\frac{y(y+1)}{y(y-2)}}{\frac{4(y+1)}{(y-2)^2}}=[/tex]

Now, you can cancel out some terms:

[tex]\dfrac{\frac{y+1}{y-2}}{\frac{4(y+1)}{(y-2)^2}}=[/tex]

Now, when you divide a fraction by another fraction, that is the same as multiplying the first fraction by the reciprocal of the second one:

[tex]\frac{y+1}{y-2}\cdot \frac{(y-2)^2)}{4(y+1)}=[/tex]

[tex]\frac{y-2}{4}[/tex]

Hope this helps!

At a particular restaurant, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories and twice as many onion rings as there are sliders. Write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal. Define the variables that you use to write the system.

Answers

Step-by-step explanation:

r = onion rings amount

s = sliders amount

system of equations

2s = r

r(70) + s(200) = 1020

(for deltamath)

This question is based on the system of equations. Therefore, the system  of equations 2s = r and r(70) + s(200) = 1020 are  that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.

Given:

At a particular restaurant, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories and twice as many onion rings as there are sliders.

According to the question,

Let the amount of onion rings be r and the amount of sliders be s.

Now, it is provided in question that, amount of sliders is twice as the onion rings. In mathematically expressed as,

⇒ 2s = r is the first system of equation.

Then, it is also give that, each onion ring has 70 calories and each slider has 200 calories. A combination meal with onion rings and sliders is shown to have 1020 total calories. This representing as,

⇒ r(70) + s(200) = 1020 is the second system of equation.

Therefore, the system  of equations 2s = r and r(70) + s(200) = 1020 are  that could be used to determine the number of onion rings in the combination meal and the number of sliders in the combination meal.

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At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys.

In simplest form, what fractions of the babies born on Tuesday were boys?

Answers

Answer:

3/4

Step-by-step explanation:

Answer:

I believe it is 3/4

Step-by-step explanation:

Simplest form right?

9/3=3

12/3=4

Ed had 35 comic books. He sold 21 comic books. What percent of his total number of comic books did Ed sell?​

Answers

60 percent because you put 21 over 35 and multiply it by 100 over 1.

Answer:

60%

Step-by-step explanation:

21/35 = x/100

x = 60

write an equation to represent the following:
five less than 1/3 a number, n. is 3



Four more than twice a number, x, is greater than the sum of three and negative seven.

Answers

1/3n-5=3 for the first one

Answer:

Five less than 1/3 a number n is 3.

[tex]\frac{1}{3}n-5=3[/tex]

Four more than twice a number x (2x+4) is greater than (>) the sum of three and a negative seven (3-7)

2x+4>3+(-7)

2x+4>3-7

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