A cone of radius 10 cm and height 16 cm is divided into two parts by a plane through the midpoint of its
axis parallel to its base. Find the ratio of the volumes of the two parts?

Answers

Answer 1

Answer:

The ratio of their volumes (the top to bottom half) is 1/7

Step-by-step explanation:

The given parameters are;

The radius, r, of the cone = 10 cm

The height of the cone = 16 cm

The point at which the cone is divided = The midpoint of the its axis and parallel to its base

The ratio of the of the volume of the two parts is given as follows;

The volume, V of the entire cone = 1/3 × Base area (π·r²) × Height, h

Therefore;

V = 1/3 × π × 10² × 16 =1600·π/3 =  1675.52 cm³

The height at which the cone is divided = 16/2 = 8 cm

The height, h₁ of the uppermost divided cone = 8 cm

The ratio of the radius to the height of the cone = 10/16 = 5/8

The radius r₁, of the uppermost divided cone = The height of the uppermost divided cone × The ratio of the radius to the height of the cone

∴ r₁ = 8 × 5/8 = 5 cm

The volume, V₁, of the uppermost divided cone = 1/3 × (π·r₁²) × h₁

∴ V₁ = 1/3 × π × 5² × 8 = 200·π/3 = 209.44 cm³

Which gives;

The volume of the lower cone, V₂ =  V - V₁

V₂ =  1675.52 cm³ - 209.44 cm³ = 1400·π/3 = 1466.1 cm³

The ratio of their volumes V₁ : V₂ = V₁/V₂ = (200·π/3)/(1400·π/3) = 209.44/1466.1 = 1/7.


Related Questions

“c.” isnt part of the question fyi
this is for AP Calculus

Answers

Answer:

  -2/3

Step-by-step explanation:

  [tex]\ln{\dfrac{1}{\sqrt[3]{e^2}}}=\ln{e^{-\frac{2}{3}}}=-\dfrac{2}{3}[/tex]

determine the prime factors of 84 in tree map​

Answers

Step-by-step explanation:

I hope i got it right...

Which type of conic section is described by the equation 4x^2 = 10 +y^2? Due in 2 HOURS, will give BRAINLIEST! A. Ellipse B. Circle C. Parabola D. Hyperbola

Answers

Answer:

c

Step-by-step explanation:

Hyperbola is the conic section described by the equation 4x² = 10 +y²

What is Parabola?

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

To identify the type of conic section from an equation whether it is circle, or ellipse a let suppose the equation as,

Ax²+By²+Cx+Dy+E=0

The given equation is 4x² = 10 +y²

4x²-y²=10

Divide the whole equation by 10

4x²/10 - y²/10=1

2x²/5- y²/10=1

x²/(1/2)- y²/10=1

The given equation is in the form of hyperbola.

Hence, hyperbola is the conic section described by the equation 4x² = 10 +y²

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-
Given the Above diagram, Find the value of x; m K
I 2y + 13
2
47
92 +1
3
14
+9
4
5
type your answer..
m type your answer
m type your answer
6

Answers

Answer/Step-by-step explanation:

m<MAH = 90° (linear pair. It is also supplementary to m<MAK = 90°)

m<MAL + m<HAL = m<MAH

Which is:

(9x + 1) + (x + 9) = 90°

Solve for x

9x + 1 + x + 9 = 90

Collect like terms

9x + x + 1 + 9 = 90

10x + 10 = 90

Subtract both sides by 10

10x + 10 - 10 = 90 - 10

10x = 80

Divide both sides by 10

x = 8

Find m<MAL

m<MAL = 9x + 1

Plug in the value of x

m<MAL = 9(8) + 1 = 72 + 1 = 73°

Find m<HAL

m<HAL = x + 9

m<HAL = 8 + 9 = 17°

HELP ASAP!! WILL MAKE BRAINLIEST!
Solve for x: −2x − 4 > 8

Select one:
a. x < −6
b. x > −6
c. x < −2
d. x > −2

Answers

Answer:

x>-6

Step-by-step explanation:

-2x-4>8

-2x>8+4

-2x>12

x>12/-2

x>-6

hope u understand : )

Someone help I’m stuck on this

Answers

Answer: 1 is 2 rectangles, 4 in a triangle and a rhombus I think.

Step-by-step explanation:

It says what would the shapes be shown as if it was split on the line.

f(x)=4x; g(x)= 4x/9 +9 please help

Answers

Answer:

F  ( 4 (   [tex]\frac{x}{9}[/tex]  ) +9  ) =  [tex]\frac{16x}{9}[/tex] +  36

Step-by-step explanation:

8. H={all numbers of the form 3n+1, for n a natural number} under multiplication?
9. J={all numbers of the form 3n+2, for n a natural number under multiplication?
10. K={perfect squares of integers) under addition?
11. L={perfect squares of integers under multiplication?
12. M = {all numbers of the form 2", for n a natural number) under addition
pol
13. N= {all numbers of the form 2", for n a natural number under multiplication?
TIMBER

Answers

Answer and Step-by-step explanation:

H= {all numbers of the form 3n+1, for n natural number} under multiplication:

Sol: all number of the form 3n+1, for n natural number so, put n=2, 3(2) +1 = 7, which is a natural number. A natural number under multiplication does not form a group because its inverse does not exist.

J= {all number of the form 3n+2, for n natural number} under multiplication:

Sol: all the number of the form 3n+2, n is the natural number does not form a group under multiplication because the identity element does not form in this set, and inverse does not exist.

K= {perfect squares of integers} under addition:

Sol: perfect square of integers under addition does not form a group because the inverse does not exist. For example, for any element x, inverse (-x) does not exist because of a square integer.

L= {perfect squares of integers} under multiplication:

Sol: a set of the perfect square of integers under multiplication is not a set, because it does not have the inverse property

M= {all numbers of the form 2, for n natural number} under addition:

Sol: natural number in the form of 2n, n is a natural number under addition is not a group as it does not have identity property. Identity property, under addition, is zero.

N= {all number of the form 2n, n is natural number} under multiplication:

All number of the form 2n, n is the natural number under multiplication is not a group. Because its inverse does not exist. For example, an element x belongs to a natural number; its inverse (1/x) does not exist in this set.

A. Interviewing college students to find what percentage expects a
job immediately after graduation
B. Collecting the cholesterol readings of a group of elderly people in
a small town
O C. Testing the effectiveness of a mouthwash by allowing one group
to use it and comparing the results with those of a group that
doesn't use it
O D. Testing the effectiveness of a hair product by allowing one group
to use it and comparing results against a control group

Answers

Answer:

B

Step-by-step explanation:

An example of a survey is A. Interviewing college students to find what percentage expects a job immediately after graduation.

What is Survey?

A survey is defined as the collection of the data or o=interpretation of the data using a list of questions asked to a particular sample of a population which determines the whole population.

From the given options, we can clearly say that C and D are not an example of a survey since survey doesn't make use of the comparison process.

In both C and D, effectiveness of mouthwash and hair product are done by comparing two groups.

So it is not a survey.

In the case of cholesterol readings, only the elderly people is taken in to account.

So, the best option is A.

Hence the survey example is Interviewing college students to find what percentage expects a job immediately after graduation.

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Find the area and perimeter of a polygon with vertices located at A(-4,-8), B(4, -8), C(4, 0), D(0, 3), and E(-4,0).

Area =

Perimeter =​

Answers

Answer:

76 and 34

Step-by-step explanation:

See attached

As we see this is a polygon with  sides of AB=BC=AE and CD=DE

Sides AB=BC=AE equal to 8Sides CD=DE = [tex]\sqrt{3^2 + 4^2}[/tex] = 5

Area is the sum of areas of a square ABCE with side 8 and a triangle CDE with base of 8 and height of 3:

Area = 8*8 + 1/2*8*3 = 64 + 12 = 76Perimeter = 8*3 + 5*2 = 24 + 10 = 34

(450) + (77) + 2395 =

Answers

Answer:

2922

Step-by-step explanation:

450 + 77 + 2395=

450 + 77= 527

527 + 2395=2922

Hope this helped!!

What are the differences and similarities between a bar graph and a histogram?

Answers

Answer:

With bar charts, each column represents a group defined by a categorical variable; and with histograms, each column represents a group defined by a continuous, quantitative variable.

Step-by-step explanation:

hope that helps


Which of the following equations have no solution? Check all that apply.
6x + 1 = 3(2x - 4)
2-5x = 7x - 12
4(3 - x) = 2(6 - 2x)
5(x + 2) = 2(x-4)
-4(x + 3) = 4(-x-1)

Answers

Hi there! :)

Answer:

Equations 1 and 5.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

We can simply each answer choice to find those which have no solution:

1.  6x + 1 = 3(2x - 4)

6x + 1 = 6x - 12

0 ≠ - 13, NO SOLUTION.

2.  2 - 5x = 7x - 12

14 = 12x

x = 7/6. 1 SOLUTION.

3.  4(3 - x) = 2(6 - 2x)

12 - 4x = 12 - 4x

0 = 0. INFINITE SOLUTIONS.

4.  5(x + 2) = 2(x - 4)

5x + 10 = 2x - 8

3x = -18

x = -6. 1 SOLUTION.

5.  -4(x + 3) = 4(-x - 1)

-4x - 12 = -4x - 4

0 ≠ 8. NO SOLUTIONS.

Therefore, the only equations with no solutions are equations 1 and 5.

Answer:

 x + 1 = 3(2x – 4) and –4(x + 3) = 4(–x – 1).

   Hope this was helpful!

Inverse Function f(x)= 5 -1/3x

Answers

Answer:

f(x)⁻¹ = -3x + 15

Step-by-step explanation:

y = -1/3x + 5

x = -1/3y + 5

x - 5 = -1/3y

(x - 5)(-3) = y

-3x + 15 = y

which best describes how to solve the equation below 64x = 37

Answers

Answer: Division

Step-by-step explanation: divide both sides by 64

divide it step by step

Simplify the expression 7 - X-(-5x) - 10 + 4x.

Answers

7-x-(-5x)-10+4x
=7-x+5x-10+4x
= -x+5x+4x+7-10
=4x+4x-3
=8x-3

Hope this can help.

Nicole charges a flat fee of $15 for babysitting plus $7 per hour a) write about equation to find the total payout. b) Evaluate an equation to find the total payout if Nicole babysits for 5 hours.

Answers

Answer:

a) t = 7x + 15

b) Nicole is paid $50 for 5 hours.

Step-by-step explanation:

flat fee = a price that will not change = $15

$7 per hour = a price of $7 for an unknown amount of hours (x) = 7x

Let "x" = amount of hours.

Let "t" = total cost.

Set the equation:

t = 7x + 15

Nicole babysits for 5 hours. Plug in 5 for x in the equation:

t = 7x + 15

t = 7(5) + 15

t = 35 + 15

t = 50

Nicole is paid $50 for 5 hours.

~

You take your car in for repairs. The service station charges $200 for parts plus $50 per hour for labor. What is the equation that models the total cost charged by the service station? y= X+​

Answers

Answer:

y=50x+200 can i get the brainliest?

Step-by-step explanation:

Please help! (Question in picture)

Answers

The answer is C. You just simplify all of the terms.

I think it is C but i'm not entirely sure sorry if its wrong gotta go

The blank
represents the input of a relation.
F Constant
G Range
H Independent Variable
J Dependent Variable

Answers

Answer:

The correct answer is H. Independent variable.

Step-by-step explanation:

The independent variable, typically represented with the variable x, is the input of the function.  In an experiment, this is the variable that the scientist changes in order to see a change in the dependent variable.  The independent variable is usually plotted along the x-axis and its values represent the domain of the function.

The dependent variable, conversely, is typically represented with the variable y, and represents the output of the function.  In an experiment, the dependent variable would represent that change that occurs due to a change in the independent variable.  The dependent variable is usually plotted along the y-axis and its values represent the range of the function.

Hope this helps!

To which subset of the real number system does the number LaTeX: 1.\overline{5}
1.
5
¯
belong?

Group of answer choices

whole numbers

irrational numbers

rational numbers

natural numbers

Answers

Answer:

[tex]\frac{1}{2}[/tex] is a rational number

Step-by-step explanation:

Given

[tex]Real\ Number = \frac{1}{5}[/tex]

Required

Determine which set of numbers it belongs to

Analyzing the options one after the other;

1. Whole numbers: 0, 1, 2, 3....

2. Natural numbers: 1, 2, 3, 4... 3.

3. Irrational numbers are numbers that can't be expressed as fractions

The option that answers this question is rational numbers because [tex]\frac{1}{2}[/tex] can be expressed as decimal and fraction interchangeable.

Hence;

[tex]\frac{1}{2}[/tex] is a rational number

Sophie plans to repaint some classroom bookcases. All of the bookcases are the same size and each requires 4 over 5 gallons of paint. If she's going to paint 16 bookcases, how many gallons of paint does she need?

Answers

Answer:

12.8 gallons of paint

Step-by-step explanation:

Multiply 16 by [tex]\frac{4}{5}[/tex]

16(4/5) = 12.8

So, she will need 12.8 gallons of paint

What is (0.83)4 rounded to the nearest hundredth?​

Answers

Answer:

3

Step-by-step explanation:

how is 9/5 - 1/3 equal 1 and 7/15. Can someone please explain and show work?

Answers

Answer:

Step-by-step explanation:

9/5=9*3/5*3=27/15

1/3=5*1/5*3=5/15

27/15-5/15=22/15=(15+7)/15=15/15+7/15

=1+7/15=1 7/15

Answer:

Below

Step-by-step explanation:

[tex]\frac{9}{5} - \frac{1}{3} \\\\\mathrm{Least\:Common\:Multiplier\:of\:}5,\:3:\quad 15\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM};\\\\\frac{9}{5}=\frac{9\times\:3}{5\times\:3}=\frac{27}{15}\\\\\frac{1}{3}=\frac{1\times\:5}{3\times\:5}=\frac{5}{15}\\\\=\frac{27}{15}-\frac{5}{15}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{27-5}{15}\\\\=\frac{22}{15}[/tex]

[tex]22\div 15 = 1 \:remainder\: 7 = \\1 \frac{7}{15}\\[/tex]

Can someone please help?

Answers

Answer:

x² - 1

Step-by-step explanation:

When x - 1 = 3 and x + 1 = 5 we know that x = 4 so (x - 1)(x + 1) = 4² - 1 when x = 4, 5² - 1 when x = 5 and so on. If you look carefully you will notice a pattern, the product is always x² - 1 so the answer to the blank is x² - 1.

Plz plz ans this with explanation

Answers

Answer:

D

Step-by-step explanation:

Least common denominator of 7 and 8 = 56

[tex]\frac{-1}{8}=\frac{-1*7}{8*7}=\frac{-7}{56}\\\\\\\frac{1}{8}=\frac{1*7}{8*7}=\frac{7}{56}\\\\\\\frac{-1}{7}=\frac{-1*8}{7*8}=\frac{-8}{56}\\\\\\\frac{1}{7}=\frac{1*8}{7*8}=\frac{8}{56}[/tex]

-8/56   , -7/56 , 7/56 ,   8/56  ,

-1/7 , -1/8 , 1/8 , 1/7

Please helpppp meeee

Answers

Answer:

AB=62, BC=61, AC=57, PR=75, PQ=52.5, QR=52.5

Step-by-step explanation:

WILL GIVE BRAINLIEST TO THE FORST PERSON WHO ANSWERS THIS!! In the diagram below, lines AB and ED are parallel. Angle < BCD is a right angle and < CBF = 125 Find angle CDE.

Answers

Answer:

35°

Step-by-step explanation:

Produce BC in the direction of C which intersects DE at any point say P.

AB || ED... (given)

So, BP would be transversal.

[tex] \therefore m\angle DPB + m\angle FBP = 180\degree\\... (By\: interior \: \angle \: Postulate) \\

\therefore m\angle DPB + 125\degree = 180\degree\\

\therefore m\angle DPB = 180\degree - 125\degree \\

\huge \red {\boxed {\therefore m\angle DPB = 55\degree}} \\

m\angle DCP = 180\degree - 90\degree \\

m\angle DCP = 90\degree \\

x = 180\degree - (90\degree + 55\degree) \\

x = 180\degree - 145\degree \\

x = 35\degree [/tex]

The value of x or the angle CDE will be 35 degrees.

What is the opposite angle theorem?

The theorem of vertical angles or angles that are vertically opposing According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.

Given that the angle CBF is 125 degrees. The value of the angle CDE will be calculated as below:-

Calculate angle ABC by using supplement angle property:-

∠ABC = 180 - 125 = 55

Draw a horizontal line PQ at point C.

Angle PCQ = 35

Angle CDE = 35

Therefore, the value of x or the angle CDE will be 35 degrees.

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10. What are the next three terms in this pattern? 4,-8, 16,
-32,
(Help)

Answers

Answer:

64 , -128 , 256

Step-by-step explanation:

in each term , -2 is being multiplied.....

Bob is buying the soccer team ice cream after their game today. 8 players want ice cream cookies and 5 players want ice cream cones. If ice cream cones cost $1.25 each and ice cream cookies cost $1.75 each, how much will Bob spend on ice cream for the team?

Answers

Answer:

Bob will spend on ice cream for the team $20.25

Step-by-step explanation:

Hello!!!

In this problem we are expected to solve for the total amount that Bob will spend to buy

8 players ice cream cookies  and

5 players ice cream cones

let us calculate as follows

Cost of ice cream cookies for 8 players = 8*1.75=  $14

Cost of ice cone for 5 players = 5*1.25=  $6.25

Total cost =  $14+ $6.25= $20.25

Anbrysoin hatchr brysonhatcher bryon hat5cher bryson hatcher btys]

Step-by-step explanation:

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