Pete runs an ice cream stand that also sells snow cones served in paper cones. The paper cones he usually uses have a radius of 3 inches and a height of 4 inches, but his supplier is out of them. As a replacement, he purchases paper cones with a radius of 4 inches and a height of 3 inches. How do the volumes of the original and replacement cones compare? A. The replacement cone holds 3π cubic inches more than the original. B. The original and replacement cones have the same volume. C. The replacement cone holds π cubic inches more than the original. B. The original cone holds π cubic inches more than the replacement.

Answers

Answer 1

Answer:

The correct answer is;

The replacement cone holds 4·π cubic inches more than the volume of the original cone  

Step-by-step explanation:

The given measurements of the cones are;

The radius of the original cone, r₁ = 3 inches

The height of the original cone, h₁ = 4 inches

The radius of the replacement cone, r₂ = 4 inches

The height of the replacement cone, h₂ = 3 inches

The volume of a cone, V = (1/3)·π·r²·h

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

∴ V₁ = (1/3) × π × (3 in.)² × 4 in. ≈ 37.7 in.³

The volume of the replacement cone, V₂ = (1/3)·π·r₂²·h₂

∴ V₂ = (1/3) × π × (4 in.)² × 3 in. ≈ 50.27 in.³

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

Volume ratio = V₁/V₂

∴ Volume ratio = (1/3) × π × (3 in.)² × 4 in. /((1/3) × π × (4 in.)² × 3 in.) = 3/4

The difference in volume, ΔV = V₂ - V₁ = (1/3) × π × ((4 in.)² × 3 in. - (3 in.)² × 4 in. = 4·π in.³

Therefore, the volume of the replacement cone is 4·π in.³ more than the volume of the original cone.


Related Questions

what 2 numbers have a product of -36 and a sum of 9

Answers

Answer: -3 and 12

Step-by-step explanation: -3+12=9 and -3(12)=-36

CAN SOMEONE PLEASEEE HELP SIMPLIFY THESE TWO EXPONENT PROBLEMS I HAVE NO CLUE HOW

Answers

Answer:

20. [tex]-\frac{y^{12} }{9x^{4} }[/tex]    

Step-by-step explanation:

21.  [tex]3 x^{2} y^{2}[/tex]

please help me figure this out!!

Answers

Do you have a Ti-84 calculator you need one to solve this problem.

Solve the system by substitution.
1. y= 7x
x − 7y = -48

Answers

Screen Shot of answer

source:Mathwa.y

Answer:

x=1

y=7

Explaination:

y=7x---------(1)* *First equation

x-7y=(-48)----(2)* *Second equation

Put (1)* into y on (2)*

x-7(7x)=(-48)

x-49x=(-48)

-48x=(-48)

48=48x

48÷48=x

1=x or x=1--------(3)* *Third equation

Put (3)* into (1)*

y=7(1)

y=7

feel free to ask me

i REALLY need answers, like if you see this PLEASE answer it

Answers

-4, -1, 1, 3, 3.9, 3.999,

The solid figure is separated along the dotted line into two rectangular prisms.
What are the volumes of the two rectangular prisms?
What is the volume of the solid figure?
Use the drop-down menus to show your answer.

The volume of two rectangular prisms are
(put the answer)
cubic inches and 128 cubic inches. The volume of the solid figure is
(put the answer)
cubic inches.

Answers

Answer:

its b easy dubs

Step-by-step explanation:

what is the next 10 numbers of pi?
3.14

Answers

Answer:

3.14159265358

Step-by-step explanation:

Answer:

3.141592653589

Step-by-step explanation:

pi = 3.14159265358979323846264338327950288419716939937510...

Answer: 3.141592653589

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x?

y=4+x
y = x − 4
y = 4 · x
y = x ÷ 4

Answers

Answer:

y=4+x  

Step-by-step explanation:

Answer: A.) y=4+x

Step-by-step explanation: Took the test :P

-4(y - 2) = 12

solve for y, thanks

Answers

Answer:

-1

Step-by-step explanation:

-4(y-2)=12

-4y+8=12

-4y=4

y= -1

-1
-4y+8=12
-8= -8
-4y=4
-1

Rosie is building a wheelchair ramp that is 24 feet long and 2 feet high. She needs to install a vertical support piece 16 feet from the end of the ramp. What is the length of the support piece in inches?

Answers

Answer:

40ft 480inches

Step-by-step explanation:

40 feet 480 inches

If the diameter of a penny is 19.05 mm on each penny is 1.52 mm thick, what is the approximate volume of the roll of the roll of pennies? Use 3.14 for pie and round your answer to the nearest tenth.

Answers

Answer:433.0mm3

Step-by-step explana

the median of a data set is 100 which statement about the data set must be true? A. the data set has an average of 100 B. Half the data values are greater than 100 C.The minimum value is 80 and the maximum value is 120 D. Only one of data points in the data points in the data has a value of 120

Answers

Answer:

B

Step-by-step explanation:

The median value is in the middle.

pls help immediately! this is due in 3 mins :/. (pls don’t give a link, i’ll give brainiest for the correct answer just pls help!)

Answers

Answer:

50 i think but i'm not 100 % sure i'm sorry

Step-by-step explanation:

15+n=-9 answer first and u will be the top one .

Answers

Answer:

[tex]n=-24[/tex]

Step-by-step explanation:

[tex]15+n=-9[/tex]

Simplify both sides:

[tex]n+15=-9[/tex]

Subtract 15 from both sides:

[tex]n+15-15=-9-15\\n=-24[/tex]

n = -24 is your final answer!

Step-by-step explanation:

15+n=-9

n=-9-15

n=-24

=-24

Please help me please

Answers

Answer:

2x+8x+6

Step-by-step explanation:

       

how do you solve this two step equation? 5 -2/3x =3​

Answers

Answer:

x = 3

Step-by-step explanation:

I will assume you meant 5 - (2/3)x = 3.  This simplifies to -(2/3)x = -2, or

(1/3)x = 1, so that x = 3.

                                                         2

"2/3x" could be interpreted as   ---------  which would give us a very different

                                                         3x                 result.  Use parentheses to

                                                                               lessen the chances of

                                                                                misinterpretation.

BRAINLIEST
a. 2 root of 5
b. 4
c. 4 root of 5
d. 3​

Answers

Answer:

4

Step-by-step explanation:

Because the height would be half of the base.

Hope this helps ^-^

Find area of square
Pls help

Answers

Answer:

49/64 yd²

Step-by-step explanation:

since where finding a square we do

A = bxh

A = 7/8×7/8

A = 49/64

Wendy and Connor each deposit 8,300 into accounts that earn 3.5% interest for 25 years Wendy's account earns annual simple interest sand Connor's account earns an annual compound interest who will earn more interest of 25 years and how much interest they will earn

Answers

Answer:

Connor will earn more interest because he is getting compound interest.

Step-by-step explanation:

I have to assume in this case that the interest is 3.5% Per year:

Simple Interest = P(r + t)

{P = Principle, r = interest rate, t = time)

Wendy = $8,300 x (3.5% x 25)

Wendy = $7,262.50 (2 d.p)

Wendy = $8,300 + $7,262.50

Wendy = $15,562.50

Compound Interest = [tex]P (1 +r )^{t}[/tex]

{P = Principle, r = interest rate, t = time)

Connor = $8,300 x [tex](1 + 0.035)^{25}[/tex]

Connor = $19,614.93

Wendy's Interest = $15,562.50 - $8,300 = $7,262.50

Connor's interest = $ 19,614.93 - $8,300 = $11,314.93

Connor earned more interest by $4,052.43

___________________________________________________

Hope this helps!

PLEASE MARK AS BRAINLIEST :)

Have a good day :)))))

When rolling a die, calculate the probability as a fraction of rolling an even number. The probability is

Answers

Answer: 3/6

Step-by-step explanation:

B
40
24
С
A
b
Find the length of “b” using
the Pythagorean Theorem.
Enter

Answers

Sorry for the bad handwriting

Anna, Boris, and Clara thought of 1 number each Ana's number increased by 20 is 21 greater than boris's number decreased by 22. Boris's number decreased by 20 is 21 greater than claras number increased by 22. How much less is claras number than annas number?

Answers

Answer:

Clara's number is 42 less than Anna's number

Step-by-step explanation:

We can start this problem out by setting our variables up:

A= Anna's number

B= Boris's number

C= Clara's number

so we can use them to build our equations. We can sepparate the problem into little more understandable pieces of information, let's start with the first piece of information:

- "Ana's number increased by 20"

A+20

- "boris's number decreased by 22"

B-22

- "21 greater than boris's number decreased by 22."

(B-22)+21

- "Ana's number increased by 20 is 21 greater than boris's number decreased by 22."

A+20=(B-22)+21

This is our first important equation here. Let's go with the second part of the problem:

- "Boris's number decreased by 20"

B-20

- "claras number increased by 22"

C+22

- "21 greater than claras number increased by 22"

(C+22)+21

Now the whole thing:

"Boris's number decreased by 20 is 21 greater than claras number increased by 22."

B-20=(C+22)+21

This is our second important equation.

So now we have the following system of equations:

A+20=(B-22)+21

B-20=(C+22)+21

We can now simplify the equations by combining like terms so we get:

Equation 1:

A+20=(B-22)+21

we can get rid of the parenthesis so we get:

A+20=B-22+21

We can subtract a 20 from both sides of the equation so we get:

A=B-22+21-20

We perform the subtractions so we get:

A=B-21

Equation 2:

B-20=(C+22)+21

We get rid of the parenthesis:

B-20=C+22+21

We add a 20 to both sides so we get:

B=C+22+21+20

We can now perform the additions so we get:

B=C+63

And now we can combine the equations. In this case we can substitute equation 2 into equation 1 to get:

A=C+63-21

We combine like terms to get:

A=C+42

We can subtract 42 from both sides to get:

C=A-42

which reads:

Clara's number is 42 less than Anna's number.

2
Which of the following expressions is equivalent to
V162?
O
27.32
36
27.1/6
.
9

Answers

Answer:36

Step-by-step explanation:

I hope this helps and if it does plz if u can buy a thanks and brainlist or what ever it’s called :)

Find missing side? Soh cah toa

Answers

Answer:

x ≈ 14.6

Step-by-step explanation:

Using the sine ratio in the right triangle

sin59° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{17}[/tex] ( multiply both sides by 17 )

17 × sin59° = x , then

x ≈ 14.6 ( to 1 dec. place )

What is the value of 2x to the power of 2 when x = 1.5?


15.0


4.45


4.50


450

Answers

Answer: 4.50 Look at the picture

Step-by-step explanation: Hope this help :D

Translate 4 units right and 3 units up.

Answers

Answer: Hope this helps! Sorry if it looks a little messy. Have an amazing day!

Step-by-step explanation:

I am confused please help. don’t use me for points.

Answers

Answer:

1. 17.2

2. 113

Step-by-step explanation:

the first answer: 17.2

the second is : 113.

i hope this helped:)

Evaluate the expression for K=-16,m=-22,and n=-23.k+m+n

Answers

Answer:

-16-22-23= -61

Step-by-step explanation:

Hope it was helpful .

Which shape below is the pre-image. How can you tell?

Answers

Answer:

the red one is the pre image because if there is two of the same letters then there is a dash behind the second letter.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST!!!!

Leslie rolls two fair number cubes numbered from 1 to 6. She first defines the sample space, as shown below:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Based on the sample space, what is the probability of getting a total of 11? (5 points)

2 over 36
3 over 36
4 over 36
5 over 36

Answers

Answer:

67

Step-by-step explanation:

Answer:

2 over 36

Step-by-step explanation:

The only way to get an 11 is with a 5 and a 6 so the probability of rolling a sum of 11 is:

(2/6)(1/6)=2/36

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