You have a cone whose height and base radius are equal and, inside it, you put the largest possible sphere that will completely fit inside. What is the exact fraction of the volume of the cone that is occupied by the sphere?

Answers

Answer 1

The exact ratio of of the volume of the cone that is occupied by the sphere is 4/(1+√2)³.

What is a cone?

A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the centre of base).

Given that the height and radius of the cone is the same.

Assume that the radius of the cone is x.

Thus the slant height of the cone is √(x² + x²) = x√2.

Assume the radius of the sphere is r.

△OEC and △BDC are similar triangles according to AAA rule.

Thus, BD/OE =BC/OC

x/r = x√2/(x -r)

Cross multiply:

x(x - r) = xr√2

x² - rx = xr√2

x² = xr√2 + rx

rx( 1+√2) = x²

r = x²/[x( 1+√2)]

r = x/ (1+√2)

The volume of the sphere is 4/3 ∏ r³ = 4/3 ∏ [ x/ (1+√2)]³

The volume of the cone is 1/3 ∏r²h = 1/3 ∏x³

The ratio of the volume of the sphere to the cone is

4/3 ∏ [ x/ (1+√2)]³ : 1/3 ∏r³

= 4 : (1+√2)³

= 4/(1+√2)³

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Related Questions

( 0) + ( -8) + (+4) =

( 0) + ( -3) + ( -4) =

Answers

Answer:

1. -4

2. -7

(don't quote the 0)

Answer:

1) -4

2) -7

Step-by-step explanation:

1) 0 + (-8) + 4 =

0 - 8 + 4 =

-8 + 4 =

= -4

2) 0 + (-3) + (-4) =

0 - 3 - 4 =

= -7

At a garage sale, a large bin full of DVDs and CDs are being sold. All the DVDs are the same price, and all the CDs are the same price.

Aleah buys 2 DVDs for $6 and 4 CDs for $8. Her friend, Ling, wants to buy 4 DVDs and 2 CDs. How much will Ling have to pay?

Aleah's brother, Pierre, wants to spend $20 on DVDs and CDs. What combination of DVDs and CDs could he buy?

Answers

Answer:

Step-by-step explanation:

$6/(2 DVDs) = $3/DVD, and $8/(4 CDs) = $2/CD

a DVD costs $3

a CD costs $2

Ling bought 4 DVDs and 2 CDs for 4×$3 + 2×$2 = $16.

Pierre bought d DVDs and c CDs for $20.

d is 0, 2, 4, or 6

c = (20-3d)/2

(d,c) = (0,10), (2,7), (4,4), or (6,1)

600 at 4% for 9 months

Answers

Answer:

Monthly payment-$67.78

Step-by-step explanation:

I didn't really know what you wanted so I just put that because that's the only thing to suit it but next time add in more information in your question please.

PLEASE HELP DUE TODAY WILL GIVE BRAINLIEST TO CORRECT ANSWER

After a few mathletes join the team, the team is able to solve 40% more problems per session. Of the team can solve 42 problems per session now, how many problem were they able to solve before the new mathletes joined?

Answers

Step-by-step explanation:

the answer is 16.8 :)hope this helps

Answer: 30 :) have a nice day!!!

Find area of composite figure 6m 10m 8m

Answers

Answer: 24

Step-by-step explanation:

Basically you just need to add them simply breaking them up then adding them

Asking for a friend please help

Answers

Answer:

=1/15

Step-by-step explanation:

this is the answer is = 1/15 hope this helps your friend out!

4x-3y=20
2x+y=30
Use the two equations above, solve for y.

Answers

Answer:

y=8

Step-by-step explanation:

Answer:

4×-3y=20

Step-by-step explanation:

chose the top one

Is this correct? Geometry Math Question

Answers

QW= 140°

hope that helped^^

How to do two step equations?

Answers

Answer:1) First, add or subtract both sides of the linear equation by the same number.

2) Secondly, multiply or divide both sides of the linear equation by the same number.

3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable.

Using the addition or subtraction property, write the equation with all terms containing the unknown in one member and all terms not containing the unknown in the other.

Factor the following expression so it is in simplest form.

6a – 4(2a + 3)

A.
–2(a – 6)

B.
–2(a + 6)

C.
2(7a – 6)

D.
2(7a + 6)

Answers

Factorization of the given algebraic expression in its' simplest form is; B.–2(a + 6)

How to factorize an Algebraic Expression?

To factorize an algebraic expression, it means that the highest common factors of the terms of the specific algebraic expression are determined and then we group the terms accordingly.

We are given the algebraic expression as;

6a – 4(2a + 3)

Multiplying the bracket out gives us;

6a - 4(2a) - 4(3)

= 6a - 8a - 12

= -2a - 12

Now, the highest common factor of the expression is 2 and so we have;

-2(a + 6)

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R(-9,4) and S(2,-1); Find T

Answers

Answer:

The question doesn’t state what T represents, so I will assume T is one of two points:

1. The midpoint of R and S, or

2. S is the midpoint of RT.

1. T((-9+2)/2,(4-1)/2)=T(-7/2,3/2)

2. T(x,y): S(2,-1)=((-9+x)/2,(4+y)/2); 2=(-9+x)/2, 4=-9+x, x=13; (4+y)/2=-1, 4+y=-2, y=-6. T(13,-6)

54 is 60% of what number? Enter your answer in the box.

PLZ HELP I WILL GIVE BRAINLIEST

Answers

Answer:

Step-by-step explanation:

you do 54 ÷ 60% = 90

check:

60% of 90 is 54 .

can I have brainliest.

The Answer XX

The Other Person Shouldn't Have Answered You Said You'd Give Brainliest And Then You Turn Around And Say You Don't Know How You Are Messed Up That Is Sad You Can Tell You Only Wanted The Answer And I'm Not Giving You The Answer To Confirm It Your Messed Up And You Are Also SELFISH

And Go Ahead And Go Off On Me Ill bLaSt Yo AyAs

Sandra has some nickels, dimes, and quarters which total $2.50. She has the same
number of nickels as quarters; however, she has twice the number of dimes as nickels.
How many of each type of coin does she have?

Answers

Answer:

5 nickels

10 dimes

5 quarters

Step-by-step explanation:

n = number of nickels

d = number of dimes

q = number of quarters

q = n

d = 2n

0.05n + 0.10d + 0.25q = 2.50

substitute

0.05n + 0.10(2n) + 0.25(n) = 2.50

0.05n + 0.20d + 0.25n = 2.50

0.50n = 2.50

n = 5

d = 10

q = 5

-2(4x – 3) = 10
Can someone help me with this math problem please

Answers

Answer:

-1/2

Step-by-step explanation:

-2(4x - 3) = 10

First distribute the -2 to 4x and -3; it turns into

-8x + 6 = 10

The subtract 6 on both sides which equals

-8x = 4

Then divide -8 on both sides...

x = -4/8 or -1/2

When 2 dice are rolled, the sum of both faces is calculated. Determine the
probability of the event: Rolling a sum of 10. Justify your answer.

Answers

Answer:

3/36 or 1/12

Step-by-step explanation:

there are a possible 36 outcomes

probability of rolling a ten has 3 chances of happening:

5, 5

4, 6

6, 4

Write the phrase "the sum of a number and twenty-three less than that number" as a mathematical expression.

A) x + 23

B) x ⋅ 23

C) x – 23

D) x + (x – 23)

Answers

Answer:

Step-by-step explanation:

The sum of a number and twenty-three less than that number" as a mathematical expression is x + (x – 23)

I mean its the only answer with sum and "less than" because that usually means you need to subtract, I hope this helps

Answer:

Step-by-step explanation:

Pls help me I’ll brainlest I need a good grade on this

Answers

Answer:12

Step-by-step explanation:

Answer:

Step-by-step explanation:

express (4+7i)(2-i) in the form a+ib

Answers

(4+7i)(2-i)

multiply it out

8-4i +14i -7i squared

i squared is the same as -1

8-4i+14i-7(-1)

8+7-4i+14i

15+10i

divide by common factor which is 5 in this case

3+2i

Starbucks opened two new locations. Location A costed $800 to open but makes $100 a month. Location B costed $1200 to open but makes $200 a month. Determine how long it will take for the locations to have made the same amount after paying off their costs and how much that amount is. *

Answers

Answer:

I think it is A that will take longer but im not 100 percent sure

Step-by-step explanation:

First write an equation:

Location A- 800+100x

Location B- 1200+200x

Then you need to plug numbers in for x

3/2+b=7/4 need help now

Answers

[tex]Answer:\\\\frac{3}{2} + b = \frac{7}{4}\\\\b = \frac{7}{4} - \frac{3}{2}\\\\b = \frac{7}{4} - \frac{6}{4} \\\\b = \frac{7-6}{4}\\\\b = \frac{1}{4}\\\\Hope \ it \ helps![/tex]

.) A group of neighborhood families are planning a trip to the museum. Tickets are $25 for adults
and $10 for children. The group also has a coupon for $5 off. The expression 25a + 10c – 5
represents the total cost for a adult and c child tickets. Monica is purchasing tickets for
5 adults and 9 children.

Answers

Answer:

$210

Step-by-step explanation:

the expression is 25a+10c-5

where a=adults,c=children

and we have 5adults and 9 children

then 25a + 10c - 5 is

25(5)+10(9)-5

=125+90-5

=210

answer:Monica is going to purchase tickets for 5adults and 9 children for$210

The flight path of a plane is a straight line from city J to city K. The roads from city J to city K run 9.4 miles south and then 15.1 miles east. How many degrees east of south is the plane's flight path, to the nearest tenth?

Answers

Answer:

Step-by-step explanation:

[tex]tan\theta =15.1/9.4\\ \\ \theta =tan^{-1}(15.1/9.4)\\ \\ \theta \approx 58.1^o[/tex]

Answer:

Step-by-step explanation:

Please I need help asap Which graph represents a scatter plot with a nonlinear negative association?

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

please helppp

Simplify.
(-2)^-3

Answers

Answer:

-1/8 <----- FRACTION

Step-by-step explanation:

-1/8
To simplify, first flip the term to the denominator to get rid of the negative exponent. Then simplify 1/-2^3. This equals 1/-8 because -2^3 is the same as -2*-2*-2, which is -8.

What is the perimeter of the shape below, given a = 5.66, b = 13.75, c = 6.76, d = 4.59

Answers

Answer:

61.52

Step-by-step explanation:

5.66+ 13.75 + 6.76 + 4.59 + 5.66+ 6.76 + 13.75 +4.59

Answer:

61.52

Step-by-step explanation:

Given the values, you can solve for the remaining sides.

a + c will equal the side on the right and b + d will equal the side at the top.

So 2(a+c) + 2(b+d) will give the perimeter.

2(5.66+6.76) + 2(13.75+4.59) = 24.84 + 36.68 = 61.52

Find the class boundaries mid point and width for the class 37-46

Answers

The mid point is 4.5 or 4 and 5 depending on how they wnat u to answer

Anyone know any music artists similar to conan gray ?

Answers

Dababy is similar to Conan gray

Answer:

Lorde, Gracie Abrams, and a few Taylor Swift songs, and if you're looking for new musicians to get into that are underrated you should definitely try Hozier, and Phoebe Bridgers.

Two teams of students are testing the effect of light on a radiometer. Team 1 finds that blue light makes the radiometer spin slower when a blue light is 35 centimeters (cm) away. To validate Team 1's test results, how must Team 2 test the radiometer?

Answers

Answer:

eafyb jdgjn sfh sg jddxhu fiuecbjz sghvhl

Answer:

It is Test it with a blue light that is 45 cm away.

Step-by-step explanation: Because it is right and I did this with my teacher and it is Test it with a blue light that is 45 cm away. hehe

Can someone help me?

Answers

Answer:

Step-by-step explanation:

5y-7=5d+3y

we will subtract 3y from both sides

5y-3y-7=5d

we will add 7 on both sides

2y=5d+7

we divide by 2

y=(5d+7)/2

y=5d/2+7/2

Answer:

Y= 5d/2+7/2

Find the common ratior for the geometric sequence and user to find the next three terms.
243, 162, 108, 72, ...

Answers

Answer:

add my sc = bmic ava, no spaces

or add my discord = XoXo_ava

Step-by-step explanation:

mom this u?

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You have a cone whose height and base radius are equal and, inside it, you put the largest possible sphere that will completely fit inside. What is the exact fraction of the volume of the cone that is occupied by the sphere?​

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You have a cone whose height and base radius are equal and, inside it, you put the largest possible sphere that will completely fit inside. What is the exact fraction of the volume of the cone that is occupied by the sphere?