A cone has twice the base diameter and three-fourths the height of a cylinder. Can you tell what the relationship between the volume of the cone and the volume of the cylinder is? Explain your reasoning.

Answers

Answer 1

Answer:

Equal volumes

Step-by-step explanation:

Given

[tex]h \to[/tex] height of cone

[tex]d \to[/tex] diameter of cone

[tex]H \to[/tex] height of cylinder

[tex]D \to[/tex] diameter of cylinder

Such that:

[tex]d = 2D[/tex]

[tex]h =\frac{3}{4}H[/tex]

Required

The relationship between the volumes

The volume of a cylinder is:

[tex]V_1 = \pi R^2H[/tex]

Where

[tex]R = 0.5D[/tex]

So:

[tex]V_1 = \pi (0.5D)^2H[/tex]

[tex]V_1 = \pi *0.25*D^2H[/tex]

[tex]V_1 = 0.25\pi D^2H[/tex]

The volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Where

[tex]r =0.5d[/tex]

[tex]r = 0.5 * 2D[/tex]

[tex]r = D[/tex]

and

[tex]h =\frac{3}{4}H[/tex]

So, we have:

[tex]V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H[/tex]

[tex]V_2 = \frac{1}{4}\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_2 = 0.25\pi D^2H[/tex]

So, we have:

[tex]V_1 = 0.25\pi D^2H[/tex]

[tex]V_2 = 0.25\pi * D^2H[/tex]

[tex]V_1 = V_2[/tex]

Answer 2

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:


Related Questions

SOMEONE HELP WITH THIS PLS

Answers

Answer:

0.1218

Step-by-step explanation:

what is n x 567 =
457 + ae
wgv - 48765

Answers

Answer:

n x 567= 567n

457+ae= 457 + ae

wgv- 48765= wgv- 48765

Step-by-step explanation:

The last 2 are the same. Since they are not like terms, they can neither be added nor subtracted. Only like can be added or subtracted

Here is a triangular prism. 4 cm 10 cm 5cm 5cm 6cm

A. What is the volume of the prism, in cubic centimeters?


B. What is the surface area of the prism, in square centimeters?​

Answers

Answer:

(A)  120 cm³

(B) 184 cm²

Step-by-step explanation:

(A)

Assuming the diagram attached is thesame as the one needed to complete the question,

Applying

V = A'×L................... Equation 1

Where V = volume of the prism, A' = Area of the triangular base, L = Length of the prism.

But,

A' = 1/2bh............. Equation 2

Where b = base of the triangle, h = height of the triangle.

Substitute equation 2 into equation 1

V = 1/2bh(L)............... Equation 3

From the question,

Given: b = 6 cm, h = 4 cm, L = 10 cm

Substitute these values into equation 3

V = 1/2(6×4×10)

V = 120 cm³

(B)

Surface area of the prism(A) = bh+L(a+b+c).............. Equation 4

Given: b = 6 cm, b = 5 cm, c = 5 cm, L = 10 cm, h = 4 cm

Substitute these values into equation 4

A = (6×4)+10(5+5+6)

A = 24+160

A = 184 cm²

4
Select the correct answer.
Which of the equations below represents a line parallel to the yaxis?
A. X= -y
B. X= 4y
C.x=y
D.X= 4
HELP

Answers

Answer:

x=4

Step-by-step explanation:

The y axis is a line where the value of x does not change ( x=0)

It is a vertical line

The only line where the value of x does not change is x=4

It is a vertical line at x=4

Jack bought a motorbike the original price was $1800 but he got a discount of 15% what was the discounted price of the bike

Answers

Answer:

$1530

Step-by-step explanation:

Hi there!

What we know

Original price was $1800There was a discount of 15%

If this motorbike was on sale for 15% off, then we know that its discounted price is 85% of the original price (100-15=85)

Then, to find the discounted price, we multiply 1800 by 85%:

1800 × 85%

Change 85% into a decimal

= 1800 × 0.85

= 1530

Therefore the discounted price of the motorbike was $1530.

I hope this helps!

BRAINIEST TO WHOEVER RIGHT

Answers

1. is false
2. is true

PLEASE HELPNI AM BEGGING YOI PLEASE!!!!!!! EXTRA POINTS AND BRAINLIEST!

Answers

Answer:

This is really tilted, and I CANNOT see! But it looks like ratio, on one of the parts. Sorry, but I don't know!

11. x>15
4. x^2 + 6 > 3
6. x>5

HELPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

[tex]16[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 8x + c[/tex]

[tex] {x}^{2} + c - 8x[/tex]

To find the c value [tex]c = ( \frac{b}{2})^{2} [/tex] , divide the coefficient of x by 2 and square the result.

[tex]( - 1 \times 4 {)}^{2} [/tex]

[tex]( - 4 {)}^{2} [/tex]

[tex]16[/tex]

Hope it is helpful....

find the minimum of the data set.

Answers

Answer:

23,600.

Step-by-step explanation:

23|6

Trina is trying to decide which lunch combination to order at a sandwich shop: 4, 5, 6, or 7. Each combination comes with the choice of an apple, an orange, or a pear. How many possible outcomes are there for a lunch combination and a piece of fruit? 4 apple orange pear 5 apple orange pear 6 apple orange pear 7 apple orange pear Type the answer in the box.​

Answers

trina is trying to decide which lunch combination to order at a sandwich shop. srry i need points

Help a n i -g g -a plz

Answers

Answer:

187.2 cm3

Step-by-step explanation:

that are many anseers

Please dont skip!! Answer please. Will give branliest. NO LINKS PLZ

Answers

Answer:

Solution given:

area of semi circle h=½πr²=½×π×5²=39.27in²

area of rectangle EFHI=l×b=6×3=18in²

area of rectangle CDFG=l×b=17×2=34in²

Total area: 39.27+18+34=91.27 square inches

Area of upper right rectangle

3(6)18in²

Area of top rectangle(square actually)

2(2)4in²

Area of bottom rectangle

5(2)10in²

Area of semicircle

πr²/2π(6+4/2)²/2π25/212.25π38.465in²

Area of middle rectangle

2(10)20in²

Total

18+4+10+38.465+2090.465in²

If you spin the spinner once, determine the probability and the likelihood of spinning with colors red, orange, blue or green, red blue orange or green, not red

Answers

Answer:

Step-by-step explanation: There are 12 colours on a spinner,

Probability of red,orange, blue or green = 1/12×4 =4/12

=1/3

Probability of red,blue, orange or green= 1/12×4=1/3

Probability of not red= 1-1/12

=11/12

In grade 8, there are 3 teachers for every 25 students. In the examination hallthe ratio of teachers to students is 15:125, Which of the following is true?

Answers

Answer:

3:25 = 15:125

15:125 is directly proportional to 3:25.

Step-by-step explanation:

PLEASE HELP! i would really appreciate it thank you
A triangle has an area of 40 cm². The base and height are scaled by a factor of 4.

The area of the resulting triangle is ___ square cm.

Answers

Answer:

7

Step-by-step explanation:

What is the length of AE?

Answers

Answer:

1.5

Step-by-step explanation:

3/2

i really need help asap show all work​

Answers

Note: Consider we need to find the factor form of the given expression by taking out the GCF.

Given:

The expression is:

[tex]-42k^3+24k^4+12k^5[/tex]

To find:

The factor form of the given expression.

Solution:

We have,

[tex]-42k^3+24k^4+12k^5[/tex]

It can be written as:

[tex]=6k^3(-7)+6k^3(4k)+6k^3(2k^2)[/tex]

Taking out the greatest common factor (GCF), we get

[tex]=6k^3(-7+4k+2k^2)[/tex]

Therefore, the factor form of the given expression is [tex]6k^3(-7+4k+2k^2)[/tex].


The table shows the distances of some places in town
from the school.
From least to greatest, order the locations by their
distance from school. From least to greatest ordered the locations by their distance from school. 1.Library- 3/5m 2.Post Office 1/2m 3.Park 3/4m 4.8/10m

Answers

4, 1, 3, 2




There you go

7. The cone shown below has a radius of 9 centimeters and a height of 12
centimeters. What is the volume of the cone?
A

Answers

The answer to this very very equation right here is 21

I need help with finding the volume of this rectangle and also what formula you used so I can understand it. Thanks

Answers

Answer:

Step-by-step explanation:

Equation

The volume formula is

V = L * W * H

Givens

From the diagram

L = 6 mi

W = 2 mi

H = 5  mi

Solution

V = 6 * 5 * 2

V = 60 cubic miles

An algebraic inequality is written in words. Which choice matches the statement?

"The product of 15 and a number, increased by 8 is at most 44."

A. 15n + 8 < 44
B. 15n + 8 > 44
C. 15n + 8 ≤ 44
D. 15n + 8 ≥ 44

Answers

Answer:

c

Step-by-step explanation:

it wouldnt be greater than or equal to because it says is at most so that means less than or equal to hope this helps

54 =. x6 picture included

Answers

9 x 6 = 54
ANSWER = 9

Plz help meeeeee…. I need to pass this

Answers

The second one I hope this helps

What is the equation of the line perpendicular to y = -x+6 that passes through the
2
point (4, 1)?

Answers

Answer:

[tex]y=x-3[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 1/2 and -2, etc.)

1) Determine the slope (m)

[tex]y = -x+6[/tex]

Looking at the given line, we can identify clearly that -1 is in the place of m, making it the slope of the line. Because perpendicular lines have slopes that are negative reciprocals of each other, we know that the slope of the line we're solving for is 1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=x+b[/tex]

Plug in the given point (4,1)

[tex]1=4+b[/tex]

Subtract 4 from both sides

[tex]1-4=4+b-4\\-3=b[/tex]

Therefore, the y-intercept is -3. Plug this back into [tex]y=x+b[/tex]:

[tex]y=x-3[/tex]

I hope this helps!

I need help please, I’m stuck

Answers

Answer:

x = 15

Step-by-step explanation:

please please help me​

Answers

i need to answer more questions to pm so i’m doing this

1 . 6 8 10

2. 18 24 30

3. 10 5 5√5

4. 5 5 5√2

5. a a a√2

6. 3√3 3 6



Solve for t.
3t- 2 = -11
A. -12
B. -11
C. -9
D.-3

Answers

Answer:

T = -3

Step-by-step explanation:

No explanation needed ...

a pizza pan has a circumference of 34.54 inches. you are making homemade pizza crust and need to know the area pf the pan to determine how much dough to make what is the area of the pan

Answers

612.515 square centimeters

WILL MARK AS BRAINLIEST!! ASAP
if y is inversely proportional to x and y = 7 when x = 9, find x when y = 14.

Answers

Y = k/x for some fixed number constant k

7 = k/9

k = 63

so Y = 63/x

14 = 63/x

14 x = 63

x = 63/14 = 9/2

2. Which of the following is the formula in solving for the area of
a circle?
A. A= 2TTI B. A= T12
C.A= id D. A=2 TT12
2
Thodi​

Answers

Answer:

πr²

Step-by-step explanation:

Answer:

formula- TTr2

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