Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 9 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?

height (h)=

radius (r)=

Answers

Answer 1

Answer:

So, The possible values of h and r are

1. r = 3 , h = 3

2. r = 1, h = 27

3. r = 2, h = 6.75

Step-by-step explanation:

P.S - The exact ques is -

As we know that Volume of cone , V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

As given,

V = [tex]9\pi[/tex]

⇒[tex]\frac{1}{3}\pi r^{2}h = 9\pi \\ \frac{1}{3} r^{2}h = 9 \\r^{2}h = 27[/tex]

So,

The possible values of h and r are

1. r = 3 , h = 3

2. r = 1, h = 27

3. r = 2, h = 6.75

In Case I-

When r = 3, h = 3

(3)² ×3 = 9×3 = 27

Satisfied

Case II-

r = 1, h = 27

(1)²×27 = 1×27 = 27

Satisfied

Case III-

r = 2, h = 6.75

(2)²×6.75 = 4×6.75 = 27

Satisfied

Noah And Lin Are Making Paper Cones To Hold Popcorn To Hand Out At Parent Math Night. They Want The Cones
Answer 2

If the radius of the base of the cone is 2 inches then the height of the cone should be 2.1485 inches.

What is the volume of the cone?

The volume of the cone is the volume occupied by the cone. It is given by the formula,

[tex]\text{Volume of the cone}= \dfrac{1}{3} \pi r^2h[/tex]

where r is the radius of the base, and h is the height of the cone.


Now, as it is given that cones need to hold 9 cubic inches of popcorn. therefore, the volume of the cone can be written as,

[tex]\text{Volume of the cone}= \dfrac{1}{3} \pi r^2h\\\\9 \times 3 = \pi r^2h\\\\\dfrac{9 \times 3}{\pi}=r^2 h\\\\8.5943 = r^2 h[/tex]

Thus, the product of the square of the radius and the height of the cone should be such that the result is 8.5943.

Now, let the radius of the cone be 2 inches, therefore, the height of the cone is,

[tex]8.5943 = r^2 h\\\\8.5943 = (2^2) h\\\\h = 2.1485\rm\ in[/tex]

Hence, if the radius of the base of the cone is 2 inches then the height of the cone should be 2.1485 inches.

Learn more about the volume of the cone:

https://brainly.com/question/1315822


Related Questions

solve for t. -1 (t + 8) = -7.1 brainly

t=___?
(Please hurry!)

Answers

Answer:

.9

Step-by-step explanation:

-1(t+8) = -7.1

PEMDAS

So times the parenthesis by -1

-t - 8 = -7.1

Add the 8 to itself to get rid of it

Then since you added it on the left, add it to the right

-t = .9

t = .9

todos los números pares son múltiplos de :
ayuda es para hoy ​

Answers

Answer:

11

Step-by-step explanation:

Creo nose XD (revisa los múltiplos de 11 siempre son pares) xd

-0.1 = -10c who can answer this

Answers

Answer:

c = 0.01 | Hope I helped :')

Steps to answer:

1. Divide both sides by -10.

-0.1/-10=c

2. Simplify  -0.1/-10 to 0.01.

0.01=c

3 Switch sides.

c=0.01

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

Checking your answer:

−0.1=−10c

1 Let c=0.01.

−0.1=−10×0.01

2 Simplify  10×0.01  to 0.1.

-0.1=-0.1

Done by NeighborhoodDealer.

write the equation of a line in slope-intercept form that has a slope of 5/3 and passes through the point (6,7)

Answers

Answer:

y=5/3x+-3

Step-by-step explanation:

please help meeeeeee​

Answers

Answer:

y=2/3x +5

Step-by-step explanation:

to find the gradient

9--1/6--9

10/15

2/3

y-y1=m(x-x1)

y-9=2/3(x-6)

y-9=2/3x-4

y=2/3x+9-4

y=2/3x+5

laurague here is your answer:)

Answers

Got it :)Thank you!!!!!!!

Solve: 5x=-6x+9
A: x= -9
B: x= -9/11
C: x= 9
D: x= 9/11

Answers

Answer:

x = 9/11

Step-by-step explanation:

5x = -6x + 9

Add 6x to both sides

11x = 9

Divide both sides by 11

x = 9/11

Answer:
X Equals 9/11

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. So X will equal 9/11, which in decimal form is 0.81.

Expand and simplify 7a + 4(a-2b)
Help please :)

Answers

Answer:

11a - 8b.

Step-by-step explanation:

7a + 4(a-2b)

= 7a + 4a - 8b

= 11a - 8b.


What is the value of the 3 in 16.35 ?

Answers

Answer:

3 tenths

Step-by-step explanation:

The face and place value of 3 in the decimal number 16.35 is, 3 and 3×10⁻¹.

What is the standard decimal form of numbers?

The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.

Each digit has a face value and a place value.

We know, A number has two values face value and place value,

Given, A decimal number 16.35.

Now, The digit 3 is one digit after the decimal,

So, It has a face value of 3 and a place value of 3×10⁻¹.

learn more about face value and place value here :

https://brainly.com/question/23719802

#SPJ2

=
Solve for x.
18+x=y
x = 0
?

Answers

18

have a nice day!!!

Answer:

The answer is 18

Step-by-step explanation:

18 + x really means 18 + 0, because x is equal to 0

and if 18 + x = y, it means 18 + 0 = y,

so y is equal to 18

hope this helped!

Four months of the year have thirty days only. What fraction of the set
of months is this?​

Answers

Answer:

4/30 or 4/120

Step-by-step explanation:

What is the standard form equation for a 1/2 line that passes though (-3,-3) and (4,2)

Answers

Answer:

y= 5/7x -2.7

Step-by-step explanation:

Y= mx + c                             (-3,-3)   (4,2)

                                           x1  , y1     x2, y2

to find m (gradient)

y^2 - y^1 / x^2 - x^1

2-(-3) / 4 - (-3)

5/7                               m = 5/7

take (4,2)  and gradient and substitute

2=5/7(4) + c

2=4.7+ c

2-4.7 = c

-2.7 = c

now we have c and m so just put it in the equation

y= 5/7x -2.7

5/7x - 14 = -22. Find x.

Answers

Answer:

x = -56/5, -11 1/5, or -11.2

Step-by-step explanation:

5/7x - 14 = -22

5x -98 = -154

5x = -154 + 98

5x = -56

x = -56/5, -11 1/5, or -11.2

Answer:

x= -11.2

Step-by-step explanation:

5/7x-14=-22

      +14 +14        Add 14 on both sides

  5/7x = -8        

(7/5)*5/7x = -8*(7/5)     Multiply by the reciprocal on both sides to leave x alone

  x= -11.2      Answer

Helpp!! Is about angles!!! Please help!

Answers

Answer:

Triangle WRD's angles are all 60 degrees, angle W and angle R and angle D.

Triangle WRD is an equiangular, equilateral triangle. It is also an acute triangle, as all angles are less than 90 degrees.

Step-by-step explanation:

You are told that WRD has all equal sides, each 3 inches long.

In a triangle, if sides are equal, then the opposite angles are also equal. So if ALL the sides are equal, then ALL the angles are equal.

The sum of the interior angles in a triangle is always 180 degrees. Since the trhee angles are all equal and they must add up to 180 degrees, 180/3 =60, so the angles must all be 60 degrees.

Triangle are classified by sides as

*** scalene = no equal sides

*** isosceles = two equal sides

*** equilateral = all equal sides

Triangles are classified by angles as

*** right triangle = one 90 degree angle

*** obtuse triangle = one angle larger than 90 degrees

*** acute triangle  = all angles less than 90 degrees

*** equiangular = all angles equal

There can be overlap in the categories, like an acute triangle also being equiangular.

A cyclist travels at an average speed of 13 mph for 3 hours.
How far did she travel in miles?

Answers

Answer:

39 miles

Step-by-step explanation:

We know that a cyclist travelled at an average rate of 13 miles per hour for 3 hours and are asked to how far she travelled in miles.

To solve, we need to take into mind that for three hours, the cyclist drove 13 miles per hour.

Meaning that for every hour, 13 miles were driven.

Therefore we need to multiply 13 by 3 to get our answer :

13 miles * 3hrs

39 miles

William can pack 60 toys in 4 hours. Find the unit rate with which he packs
toys.
A.16 toys/hour
B.15 toys/hour
C.14 toys/hour
D.13 toys/hour

Answers

the answer is
b. 15 toys/hour

Write the equation of the line, in slope-intercept form, with the
following information:
slope: -1
y-intercept: (0, -1)

Answers

Answer:

y = -x -1

Step-by-step explanation:

x1= 0, y1= -1

[tex]slope = \frac{x - x1}{y - y1} = \frac{x - 0}{y - ( - 1)} = \frac{x}{y + 1} [/tex]

-1 = x/(y+1)

-1 (y+1) = x

y+1 = -x

y= -x -1

Can you solve for a, b and c?
20 – 3b = -5
4a + 3b = 17
50 - 2a = 1

Answers

Answer:

c  =  1 ,  a  =  2,  b  =  3

Step-by-step explanation:

3x^2+9x+27x^3 pls help the ^ means exponent

Answers

Answer:

27x^3+3x^2+9x

Step-by-step explanation:

please help!!!!!! i need this done asap!!! brainliest to whoever answers!!

Answers

Answer:

volume = Pi(2x^2+3x-5) x (2x+5)^2    or     P1(8x^4+52x^3+100x^2-125)

Step-by-step explanation:

radius = (4x+10)/2 = 2x+5

volume = Pi(2x^2+3x-5) x (2x+5)^2

volume = Pi(2x^2+3x-5) x (4x^2+20x+25)

volume = P1(8x^4+52x^3+100x^2-125)

erin has 40,000 in a savings account that earns 15% interest per year. the interest is not compounded. how much will she have in 3 months?

Answers

Answer:

$41500

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 15%/100 = 0.15 per year,

putting time into years for simplicity,

3 months ÷ 12 months/year = 0.25 years,

then, solving our equation

I = 40000 × 0.15 × 0.25 = 1500

I = $ 1,500.00

The simple interest accumulated

on a principal of $ 40,000.00

at a rate of 15% per year

for 0.25 years (3 months) is $ 1,500.00.

What is equivalent to 4x + 6y

Answers

Answer:

Is that all...

Step-by-step explanation:

Is there any other information if not then it is impossible to answer that question.

What is the equation for the line in slope -intercept form?

Answers

Answer:

I can't see it

Step-by-step explanation:

We need a bigger picture.

The graph shows a proportional relationship between the distance a car travels and the fuel it consumes.

Based on the graph, the car requires___gallons of fuel to travel 100 miles.

A. 1.0
B. 2.5
C. 4.0
D. 5.5

Answers

1/40 = x/100
100=40x
x=2.5

I really neeed help ... please help me

Answers

Answer:

fist one is 36 and the second one is 238

Step-by-step explanation:

to find volume multiple length times width times height though in this case you only need to multiple two numbers to get the answer

Sam had 225 grams of raisins. After buying another two bags of raisins he then had
175 grams of raisins
He writes this equation where r represents number of bags of raisins to describe how
225r+2=1475
Is he correct? Explain your answer.
How many grams of raisins were in one bag?

Answers

Answer: No, he is not correct, the correct equation is:

225 + 2*r = 1475

Solving that, we can find that each bag of raisins has 625 grams of raisins.

Step-by-step explanation:

I suppose that the problem is as follows:

"Sam had 225 grams of raisins. After buying another two bags of raisins he then had  1475 grams of raisins"

Then, if each bag of raisings has r grams of raisings, two bags will have two times that, or:

2*r grams of raisings.

Then if we take what he had at the beginning, and we add these 2*r grams, we should get the 1475 grams that he has at the end:

225 + 2*r = 1475

This is what he should get.

and we can solve it for r, to get:

2*r = 1475 - 225 = 1250

r = 1250/2 = 625

r = 625

This means that each bag of raisins has 625 grams of raisins.

But instead, he got:

225*r + 2 = 1475

In this case, he multiplied his previous amount of raisings by the amount that each bag has, so his equation is wrong.

An alarm rings 8 times in 5 seconds. What is the unit rate ,in rings per second?

Answers

1.6 rings per second
1.6 per second hope this helped!!! it’s 5 divided 8. ( 8/5=1.6 )

Someo ne pllllzzzz help me asap i will give brain thingy and 20 points!

Answers

Part 1) Finding the inverse

Let x = r and y = H(r)

We have the equation y = 6240(1 + x/100)^t which is the same as saying y = 6240(1 + 0.01x)^t since 1/100 = 0.01

From here, swap x and y to get the equation x = 6240(1+0.01y)^t

Let's solve for y

x = 6240(1+0.01y)^t

6240(1+0.01y)^t = x

(1+0.01y)^t = x/6240

1+0.01y = (x/6240)^(1/t)

0.01y = (x/6240)^(1/t)-1

100*0.01y = 100*((x/6240)^(1/t)-1)

y = 100*((x/6240)^(1/t)-1)

y = 100*(x/6240)^(1/t) - 100

This becomes r = 100*(H/6240)^(1/t) - 100 after we replace y with r and x with H. Note the r and H swapped places, just like x and y did. Earlier we had H isolated on the left, but now r is isolated on the left.

We could write r(H) = 100*(H/6240)^(1/t) - 100 to mean the same thing.

So what exactly does this inverse function do? Well the original function tells us the number of households for any given growth rate, which is r.

The inverse function swaps things around to allow us to find the growth rate if we know how many households there are. We're working backwards. In both cases, t is held to some constant fixed value.

===========================================================

Part 2) Finding the growth rate if the number of households is 7800 after 3 years.

We're going to plug in H = 7800 and t = 3 into the inverse function we found to determine the value of r, or r(H)

r(H) = 100*(H/6240)^(1/t) - 100

r(7800) = 100*(7800/6240)^(1/3) - 100

r(7800) = 7.72173450159419

You'll need your calculator to get this approximate value. After rounding to two decimal places, we get r(7800) = 7.72

Since r = 7.72, this means the growth rate is 7.72%

Help NOW PLEASE



Joy multiplied (3x – 3) by a
second binomial. If the product
was 9x2 – 18x + 9, find the
second binomial.
A. (3x – 3)
B. (3x + 3)
C. (3x – 6)
D. None of the above

Answers

Answer

(3x-3)

Step-by-step explanation:


What is the measure of

Answers

Answer:

<Ber=<kem(vertically opposite angle)

9x-17=3x+31

9x-3x=31+17

6x=48

x=48/6=8

<kem=3×8+31=55°is answer

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