A square pyramid is inscribed in a rectangular prism. A cone is inscribed in a cylinder. The pyramid and the cone have the same volume. Part of the volume of the rectangular prism, 1 V 1 , is not taken up by the square pyramid. Part of the volume of the cylinder, 2 V 2 , is not taken up by the cone. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?

Answers

Answer 1

Answer:

V₂ = V₁

Step-by-step explanation:

Let the height of the rectangular prism = h

Let s represent the side length of the base of the square prism, we have;

The volume of the prism, [tex]V_{prism}[/tex] = s²·h

The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h

∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]

∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h

Similarly, for the cylinder, we have;

Let h represent the height of the cylinder

Let r represent the radius of the base of the cone, we have;

Therefore;

The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h

The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h

∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h

V₂ = (2/3)·π·r²·h

[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]

Therefore;

(1/3)·π·r²·h = (1/3)·s²·h

∴ π·r² = s²

Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁

V₂ = V₁.


Related Questions

Please help me solve this problem

Answers

multiply both sides by lh, V=wlh

Answer:

V = wlh

Step-by-step explanation:

Given

w = [tex]\frac{V}{lh}[/tex] ( multiply both sides by lh to clear the fraction )

wlh = V

Can some help with this problem

Answers

30
As it an equilateral so it would be 60
Its split into two 60/2 = 30

the principal argument of z = —4+i4√3 is​

Answers

Answer:

Let z=−4+0i. Then, ∣z∣=

(−4)

2

+0

=4

Clearly, the point (−4,0) representing z=−4+0i lies on the negative side of real axis. Therefore, principal argument of z is π.

You are selecting meals for a school event and you are planning on at least 240 students at this event. The chicken meal will cost $5 and the beef meal will cost $8 per serving. Your total budget is $1200.00. Select a system of linear inequalities that shows the various numbers of Chicken and Beef meals you can prepare. Let x = number of chicken meals and let y = number of beef meals.

Answers

Answer:

x + y ≥ 240

5x + 8y ≤ 1200

Step-by-step explanation:

Assume;

Number of chicken meals = x

Number of Beef meals = y

Total budget = $1200

Find:

Inequality

Computation:

Number of chicken meals + Number of Beef meals  ≥ Total students

x + y ≥ 240

Total cost = (Number of chicken meals)(Cost of chicken meal) + (Number of Beef meals)(Cost of beaf meal)

5x + 8y ≤ 1200

Choose the answer that is equivalent to the quotient.
(-4x3 + 16x2 21x + 22) divided by (2x – 3)
0-222 +51 - 3+
13
21-3
o 22 – 3+3
O-212 + 52 - 3+
16
21-3
0-222 + 52 - 3

Answers

I believe it would be B sorry if I’m wrong

What is the product?

Answers

21x^7y^11 ur welcome cuh

find the area of the rhombus. pic included, thank you

Answers

Answer:

80in 2

Step-by-step explanation:

Answer:

a=(d1×d2)÷2

(20×12)÷2

240/2

120

Sandra y José son dos amigos que se encuentran en diferentes partes de la ciudad de Lima (Observa el plano), la distancia que los separa en el plano es de 7 cm ellos quisieran saber ¿Cuál es la distancia real en metros que los separa? Sabiendo que el plano ha sido dibujado a escala 1: 20 000.

Answers

Respuesta:

1,4 kilometros

Explicación paso a paso:

Dado que :

Distancia que separa a Sandra y José en el mapa = 7cm

Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.

Por tanto, una distancia de 7 cm en el mapa será:

20.000 * 7 = 140.000 cm en el suelo = distancia real

Por lo tanto, la distancia real = 140.000 cm.

Recordar :

1 cm = 10 ^ -5 km

140000 cm = 1.4 kilometros

Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.

Sort each function into the correct category.

Linear Functions

Quadratic Functions

Exponential Functions

f(x) = 0.45X-1

f(x) = 5

f(x) = 4.5x +18

Rx) = 19x2

f(x) = x² – 3x+4

f(x) = 2x - 6

Answers

Answer:

Linear functions are

f(x) = 0.45 x - 1

f(x) = 5

f(x) = 4.5 x + 18

Quadratic function is

R(x) = 19x^2

Step-by-step explanation:

The linear function is a function in which the degree of function is 1.

So,

f(x) = 0.45 x - 1

f(x) = 5

f(x) = 4.5 x + 18 are the linear functions.

The quadratic function is a function in which the degree of function is 2.

So,

R(x) = 19 x^2 is a quadratic function.

The exponential function is a function which involves the exponents.

Answer:

pic

Step-by-step explanation:

find 22×28×25×30 in acres?

Answers

Answer:

22x 28 x 25 x 30 = 462000

whats are the units.....cm or m

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{22(28)(25)(30)}\\\large\textsf{22(28) = \bf 616}\\\large\textsf{616(25)(30)}\\\large\textsf{616(25) = \bf 15,400}\\\large\textsf{15,400(30)}\\\large\textsf{ = \bf 462,000}\\\\\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 462,000}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
what is the greatest number of bracelets she can buy?

Answers

The greatest number of bracelets she can buy is 63
It’s 63 , because when you subtract 50-12 you get 38, and then when you divide 38 into .60 you get 63.333... and you can’t buy a .33 of a bracelet so it’s going to be 63.

The vertex of this parabola is at (-1,-3). Which of the following could be its
equation?
(-1, -3)
O A. X=-2(y+3)2-1
B. x=-2(y - 3)2 - 1
C. X=-2(y + 1)2-3
D. X = -2(y - 1)2-3

Answers

Answer:

Step-by-step explanation:

Y equals mx plus b

Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Answers

Answer:

(1/3) r2 =(1/3) r +14

1/6 divided by 83 r + 14

97r

i think...

I hope this helps you!

XoXo Mashayla

Step-by-step explanation:

what is the slope of the line shown below (6, 6) (1, -4)

Answers

Answer:

2

Step-by-step explanation:

To find the slope of a line, you must get two points off the line

Two points will be: (6, 6) and (1, -4)

Then use the Slope-Formula to solve for the slope of the line

m = slope
m = y2-y1/x2-x1
m = -4-6/1-6
m = -10/-5
m = 10/5
m = 2

The Slope of the line is 2

Answer:

2

Step-by-step explanation:

if you're looking at the table and you heard of rise/run, your rise is -10 if you go down from (6,6) and -5 if you go left to reach (1,-4). That will give you -10/-5 which gives you a positive 2. it would be the same if you went up 10 from (1,-4) and then 5 right to reach (6,6).

If f(x) = k where k is a constant, and the points (6,1) and (8,1) lie on the graph of y = f(x), what is the value of f(0)?
I think the answer is 1 but not 100% sure.

Answers

Answer:

The value of f(0)=1

Step-by-step explanation:

We are given that

[tex]f(x)=k[/tex]

[tex]y=f(x)[/tex]

(6,1) and (8,1) lies on the graph of y=f(x)

We have to find the value of f(0).

[tex]f(6)=1[/tex]

[tex]f(8)=1[/tex]

[tex]f(x)=k[/tex]

By comparing ,we get

k=1

Therefore, [tex]y=f(x)=1[/tex]

Now, substitute x=0

[tex]f(0)=1[/tex]

Hence, the value of f(0)=1

The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28

Answers

Answer

6x<-12

Step-by-step explanation:

Answer:

There would be 2 answers in this case:

C. 6x > 32

and

D. 21 + x < 28

Step-by-step explanation:

A. Incorrect

6-13 = -7, and -7 is NOT greater than 7

B. Incorrect

6(6) = 36, and 36 is NOT less than -12.

C. Correct

6*6 = 36, which is greater than 32.

D. Correct

21+6 = 27, which is less than 28.

(-9g5+ 9) + (4g5- 5)

Answers


−9​g5+9+4g5−5

−9g5+4g5+9−5

−5g5+9−5

Answer: −5g5+4



evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5

Answers

Answer:

option 2. -1 1/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 1/4x

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                           f(-5) = 1/4(-5)Multiply:                                                                                                             f(-5) = -5/4Simplify:                                                                                                             f(-5) = -1 1/4

measured the volume of an object and recorded it as 46 cubic cm
which was 15% high from the actual volume. Find the actual volume.

Answers

Answer:

[tex]40\ cm^3[/tex]

Step-by-step explanation:

Let the actual volume is V.

The measured volume of an object is 46 cubic cm  which was 15% high from the actual volume.

According to the given condition,

[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]

So, the actual volume was [tex]40\ cm^3[/tex].

A sum of money earns the interest ar the rate of Rs. 5 per Rs.25 in a year. how many years would it trible itself?
a. 5
b. 10
c.15
d. 20​

Answers

the sun to this is d. 20

Simplify 5^3 x 5^4

5^12
5^7
25^12
25^7

Please help ASAP. Please. The answer is one of those above.

Answers

Answer:

5⁷

Step-by-step explanation:

5³×5⁴

when bases are same powers are added

so..

5(³+⁴)

5⁷

Answer:

5^7

Step-by-step explanation:

Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)

You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!

What is 8 x 3 + 10 - 13 x 2? Show your work.
Will give first answer brainliest

Answers

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

Find the measure of the indicated angle.

Answers

2x + 40 = 180

2x = 140

x= 70

answer is 70

During his lunch hour, Matt asked 24 students how many after-school activities they participated in. This list shows the survey results.

Answers

Answer:

[tex]Ratio = 1 : 6[/tex]

Step-by-step explanation:

Given

[tex]n = 24[/tex]

Results:

[tex]1, 2, 0, 0, 3, 2, 4, 2, 1, 4, 3, 2[/tex]

[tex]1, 1, 2, 1, 0, 3, 3, 2, 4, 1, 1, 0[/tex]

Required

Ratio of students not participating to all students

Students not participating are represented with 0;

So, we have:

[tex]n(0)= 4[/tex]

The ratio is then calculated as:

[tex]Ratio = n(0) : n[/tex]

[tex]Ratio = 4 : 24[/tex]

Divide by 4

[tex]Ratio = 1 : 6[/tex]

Which must be true of a quadratic function whose vertex is the same as its y-intercept?

Answers

Answer:

A

Step-by-step explanation:

because y-intercept is when x=0, so right on the y axis.

Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
O A. Midpoint
O B. Ordered pair
O C. Coordinate
O D. Vertex

Answers

The answer should be A midpoint

Find the length of UC

A. 54
B. 4
C. 39

Answers

Answer:

54

Step-by-step explanation:

It is the answer to this question

Wait waaaait Hol' up.

Answer:

Its 18.

A tower is 543m from your house. The angle of elevation to the top of the tower is 33.4°. How high is the tower?

Answers

Answer:

358

Step-by-step explanation:

the step by step is in the photo so look at it

358 is the correct answer

Can someone please help me with this?

Answers

Answer is x=1.5 100% jus took it lol

30g of cornflakes contain 2.5 grams of fat how many grams of fat are there in 320g of cornflakes

Answers

Hello :)

Use proportionality

We know that :

30g of cornflakes ⇒ 2.5g of fat

320g of cornflakes ⇒ xg of fat

x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat

Have a nice day!

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