A cone fits inside a square pyramid as shown. For
every cross section, the ratio of the area of the circle to
Since the area of the circle is the area of the
square, the volume of the cone equals
the area of the square is
or 7
402
o the volume of the pyramid or - Alenchor
arh.
Cross section
r
o the volume of the pyramid or
+(1200)
2n.
o the volume of the pyramid or z { nºm) or
7
2r
2r
22h.
0 Į the volume of the pyramid or = { 29°m) oraz
arh.
m no

A Cone Fits Inside A Square Pyramid As Shown. Forevery Cross Section, The Ratio Of The Area Of The Circle

Answers

Answer 1

The volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

The ratio of the area is given as:

[tex]R= \frac{\pi r^2}{4r^2}[/tex]

or

[tex]R= \frac{\pi}{4}[/tex]

The volume of a cone is:

[tex]V_1 = \frac 13 \pi r^2 h[/tex]

For a pyramid, the volume is:

[tex]V_2 = \frac 43 r^2h[/tex]

Rewrite as:

[tex]V_2 = 4 * \frac 13 r^2h[/tex]

Divide by 4

[tex]\frac{V_2}{4} = \frac 13 r^2h[/tex]

Substitute [tex]\frac{V_2}{4} = \frac 13 r^2h[/tex] in [tex]V_1 = \frac 13 \pi r^2 h[/tex]

So, we have:

[tex]V_1 = \frac{V_2}{4} * \pi[/tex]

This gives

[tex]V_1 = \frac{\pi}{4} V_2[/tex]

Hence, the volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

Read more about volumes at:

https://brainly.com/question/9554871


Related Questions

Janelle makes a profit of 10% when she sells a bag for $900
i. What is the cost price? ii. find out how much she should have sold it for to make a profit of 15%​

Answers

Answer:

i. 818.18

ii. 940.9

Step-by-step explanation:

SP = 900

or, CP + 10% of CP = 900

or, CP + 10/100 × CP = 900

or, 110CP = 90000

or, CP = 90000/110

CP = 818.18

for profit= 15%

SP = 9000/11 + 15% of 9000/11

= 940.9

John buys a bag containing 3 pounds of flour. He uses 12 ounces of the flour for a craft project. How much flour is left in the bag?

PLEASE ASAP

Answers

Answer:

36 ounces

Step-by-step explanation:

3 pounds is 48 ounces - 12 pounds used gives you 36 ounces which is 2 pounds and a quarter ( 2 1/4)

2/3 divided by 3/6 is : help asap​

Answers

the answer is 4/3 OR 1 1/3 :)

2/3 / 3/6= 1 1/3
Let me know if you need me to show how to solve it

the roof of the clock tower is a square pyramid each side of the base is 16 ft the slant height is 22 ft what is lateral area of the roof​

Answers

Answer:

Need more points lang sorry

50 points! Given the vertices A(-4,6), B(6,6), C(6,2),find the circumcenter. I will mark brainliest. Random answers will be reported

Answers

Answer:

(1, 4)

Step-by-step explanation:

The circumcenter is the intersection of the perpendicular bisectors.

Find the two equations for the perpendicular bisectors and solve the system for intersection point.

Given the vertices A(-4,6), B(6,6), C(6,2)

Find the slope and midpoint of AB and BC

m(AB) = (6 - 6)/(6 - (-4)) = 0, this is a horizontal segment

M(AB) is

x = (-4 + 6)/2 = 1, y = (6 + 6)/2 = 6

Perpendicular bisector is a vertical line that passes through (1, 6) so its equation is:

x = 1

m(BC) is undefined as x-coordinates are same, so the segment is vertical

M(BC) is

x = (6 + 6)/2 = 6, y = (6 + 2)/2 = 4

Perpendicular bisector is a horizontal line that passes through (6, 4) so it is:

y = 4

The intersection of the lines x = 1 and y = 4 is the point (1, 4)

The circumcenter is point (1, 4)


1. At best buy they have a 50" TV that sells for $1450 and is on sale for 20% and sales tax is
7.5%. What is the final cost?

Answers

i think it’s 1,247. explanation: take 20% of 1450 and subtract it since it’s on sale, giving you 1160 after subtracting 290. then, take 7.5% of 1160 and add it. 7.5% of 1160 is 87, so if you add 87 to 1160, you get $1,247. hope this helped!
$1225 that’s the answer i got it right on the plato

Josie watches a play at the theatre.
The play ends at 9:55 pm.
It takes Josie 15 minutes to get from her seat in the theatre to the bus stop.
Buses to Josie's home leave the bus top at the following times
18:25
19:25
20:25
21:05
21:25
22:05
22:25
a)
Write down the time of the earliest bus that Josie can catch.
b) How long will Josie have to wait at the bus stop for, if she catches the
earliest possible bus?

Answers

Answer:

22:25

She will wait for 15 min

Step-by-step explanation:

9:55 is 21:55 in 24h time

after 15 min it will be 22:10

the closest time will be 22:25

25-10 is 15

15 min waiting

(6x^2+3x) + (x^2 - 4x -3)
plz help

Answers

Answer:

7x^2 - x -3

Step-by-step explanation:

(6x^2+3x) + (x^2 - 4x -3)

We have to use distributive property first to get rid of the parenthesis, so you simply have to multiply the positive (+) symbol with everything inside the second set of parenthesis.

+ * x^2 = x^2

+ * -4x = -4x

+ * -3 = -3

Now, we rewrite the equation which is

6x^2 + 3x + x^2 - 4x -3

Now you simply combine like terms.

6x^2 + x^2 = 7x^2

3x-4x = -x

The answer will be

7x^2 - x -3

Hope this helps!!

-Ketifa

(Can I get brainliest?)

Martina runs 8 miles in 72 minutes.
How many minutes does she take per mile?

Answers

Answer:

9 minutes per mile

Step-by-step explanation:

72/8 = 9 min/mile

Which equation has no solution?

13y+2-2y=10y+3-7
9(3y+7)-2=3(-9y+9)
32.1y+3.1+2.4y-8.2=34.5y-5.1
5(2.2y+3.4)=5(y-2)+6y

Answers

Answer:

D has no solution

I hope this helps a little bit.

Find the value of x.

Answers

Answer:

x = 13

Step-by-step explanation:

3x + 5 = 44

3x = 39

x = 13

please help!!! will mark brainliest

Answers

the second choice...... Let me know if it’s right

Answer:

2nd one I believe

Step-by-step explanation:

Subtract.
(2/9v)-(-1/3v+5/9)

Answers

Answer:

Use Desmos the calculator

Step-by-step explanation:

Answer: 5 ( x - 1) / 9

Which words correctly complete the statement below?
APOR is dilated with the center of dilation at the origin and a scale factor of 0.5 to
obtain AP'O'R' The triangles' corresponding angles are
and their
corresponding sides are
therefore, the triangles are
congruent; proportional; similar
congruent; congruent; congruent
proportional; proportional; similar
proportional; congruent; congruent

Answers

Answer:

congruent; proportional; similar

Step-by-step explanation:

Lana has completed 65% of her math homework. Which fraction is equivalent to 65%?
A. 13/20
B. 65/1
C. 7/20
D. 13/2,000

Answers

Answer:

A) [tex]\frac{13}{20}[/tex]

Step-by-step explanation:

[tex]\frac{13}{20} = 065 = 65%[/tex]%

[tex]\frac{65}{1} = 65 = 100%[/tex]%

[tex]\frac{7}{20} = 035 = 35[/tex]%

[tex]\frac{13}{2,000} = 0.0065 = 0.0065[/tex]%

help with this question please

Answers

C because -7 is the biggest and x is smaller
The answer is C............

Welp, the last one before the test

Answers

Answer:

y=2x-3

Step-by-step explanation:

y=mx+c

m=gradient=

5-(-5)/4-(-1)

=10/5

=2

c=y intercept=-3

y=2x-3

Answer:

y = 2x - 3

Step-by-step explanation:

(4, 5) and (0, -3)

m=(y2-y1)/(x2-x1)

m=(-3-5)/(0-4)

m=(-8)/(-4)

m=2

y - y1 = m(x - x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

The staircase has three identical parallelogram-shaped panels. The horizontal distance between each panel is 4.25 inches. The area of each panel is 287 square inches. What is the value of x ?

Answers

*see attachment for diagram

Answer:

x = 20.5 in.

Step-by-step explanation:

What we are requested to find is the height of the panel/parallelogram = x

Area of each panel = base × height = 287 in.²

Given that the total length of the 3 panels which includes the length of the 2 gaps within them = 50.5 in., first, let's find the base length of each panel.

Base length of each panel = (total length - length of the 2 gaps in between the 3 panels) ÷ 3

= (50.5 - 2*4.25) ÷ 3

= 42 ÷ 3

Base length of each panel = 14 in.

✔️Next is to find the height of the panel, x.

area of parallelogram = base × height

Base = 14 in.

height = x

Area = 287 in.²

Plug in the values

287 = 14 × x

287 = 14x

Divide both sides by 14

287/14 = x

20.5 = x

x = 20.5 in.

The graph shows a line and two similar triangles.

What is the equation of the line?

A. Y=3/2x
B. Y=2/3x
C. Y=3x
D. Y=2x​

Answers

Answer:

a y=3/2× Pls help me do me one

a

Graph the equation y = 4x − 5 using slope and y−intercept.


on a graph

Answers

ANSWER:
The picture below is an image of what the graph should look like. Hope this helps!

find the value of x?

Answers

Answer:

30

Step-by-step explanation:

The sum of the angles of a triangle is 180

x+34 +116 = 180

Combine like terms

x+150 = 180

Subtract 150 from each side

x+150-150 = 180-150

x = 30

using the angle sum property of triangle.

According to this, sum of all angles of a triangle is equal to 180°

x° + 116° + 34° = 180°

x° + 150° = 180°

x° = 180° - 150°

x° = 30°

A right square prism has a volume of 220 cubic meters. The prism is enlarged so its height is increased by a factor of 10, but the other dimensions do not change. What is the new volume?
A. 2200m³
B. 1450m³
C. 1200m³
D. 1580m³

Answers

B. Is the correct answer

Answer:

B.

Step-by-step explanation:

your welcome

Joy and Joey share a 18-ounce bucket of clay. By the end of the week, Joy has used
1
6
of the bucket, and Joey has used
2
3
of the bucket of clay. How many ounces are left in the bucket?

Answers

3 ounces
explanation: 1/6 of 18 is 3 so 18-3= 15 and 2/3 of 18 is 12 so 15-12=3 ounces

find lcm of 7 by 24 and 17 by 36​

Answers

Step-by-step explanation:

LCM for 7 by 24=168

LCM for 17 by 36=612

Which one should I choose?

Answers

Given:

A figure of a quadrilateral.

To find:

The measures of angle 1 and angle 2.

Solution:

The given figure has two pairs of congruent adjacent sides. So, the quadrilateral in the figure is a kite.

We know that the diagonals of a kit are perpendicular to each other at the point of intersection.

[tex]m\angle 1=90^\circ[/tex]

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

[tex]90^\circ+65^\circ+m\angle 2=180^\circ[/tex]

[tex]155^\circ+m\angle 2=180^\circ[/tex]

[tex]m\angle 2=180^\circ-155^\circ[/tex]

[tex]m\angle 2=25^\circ[/tex]

Therefore, the correct option is C.

Evaluate the following expression when x = 3 and y = 4:
2x + y2 - 1

Answers

Answer:

21

Step-by-step explanation:

x = 3

y = 4

2x + y² - 1

2(3) + 4² - 1

2(3) + 16 - 1

6 + 16 - 1

22 - 1

21

Jack purchases 4 pounds of colby jack cheese if the price is $ 5.98 per pound how much did jack pay

Answers

Answer:

$28.92

Step-by-step explanation:

4 x 5.98

Answer:

23.92

Step-by-step explanation:

5.98 (4) = 23.92

Find the slope using points ( 7,-3) and (11,-4)

Answers

Answer:

1/4

Step-by-step explanation:

Answer:

m = [tex]-\frac{1}{4}[/tex]

Step-by-step explanation:

Use the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1 , y_1) = (11 , -4)\\(x_2 , y_2) = (7 , -3)\\[/tex]

Plug in the corresponding numbers into the corresponding variables:

slope (m) = [tex]\frac{-3 - (-4)}{7 - 11} = \frac{-3 + 4}{7 - 11} = \frac{1}{-4} = -\frac{1}{4}[/tex]

[tex]-\frac{1}{4}[/tex] is your answer.

~

What is arc BDE?
Links=reported
Plz helppp!!

Answers

Answer:

around 228 degrees

Step-by-step explanation:

Answer: 143

Step-by-step explanation:

SOMEONE HELP!!!!!!!!!!!!!!!

Answers

Answer:

Q= 5c

Step-by-step explanation:

Q=5c ........................
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