If a sphere of ice cream that was 2.5 inches in diameter was placed on top of the ice cream cone that had a height of 4 inches and a diameter of 1.75 inches and left to melt directly into the cone, would the all of the ice cream fit into the cone? Justify your answer using mathematics and a complete sentence answer.

Answers

Answer 1

Answer:

The cone would not the all of the ice cream fit into the cone.

Step-by-step explanation:

Geometrically speaking, the volume of the cone ([tex]V_{c}[/tex]), measured in cubic inches, is described by the following equation:

[tex]V_{c} = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Base radius, measured in inches.

[tex]h[/tex] - Height, measured in inches.

And the ice cream ball is described by the volume equation for the sphere ([tex]V_{s}[/tex]), measured in cubic inches:

[tex]V_{s} = \frac{4\pi}{3} \cdot R^{3}[/tex] (2)

Where [tex]R[/tex] is the radius of the ice cream ball, measured in inches.

In this case, the ice cream will fit into the cone if and only if [tex]V_{s} \le V_{c}[/tex]. That is:

[tex]\frac{4\pi}{3}\cdot R^{3} \le \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]

[tex]4\cdot R^{3} \le r^{2}\cdot h[/tex]

If we know that [tex]r = 0.875\,in[/tex], [tex]h = 4\,in[/tex] and [tex]R = 1.25\,in[/tex], then the inequation is:

[tex]4\cdot (1.25\,in)^{3}\le (0.875\,in)^{2}\cdot (4\,in)[/tex]

[tex]6.25\,in^{3}\le 3.063\,in^{3}[/tex] (CRASH!)

Which leads to an absurd. Hence, the cone would not the all of the ice cream fit into the cone.


Related Questions

Order the following rational numbers from greatest to least. 2.5, 0.3, -4.5, -2.9, 4.3, -6.2, -1.4, 5.3, -3.5, 1.8 *

Answers

Answer:

5.3, 4.3, 2.5, 1.8, 0.3, -1.4, -2.9, -3.5, -4.5, -6.2

Step-by-step explanation:

Xavier walked 8 miles in 5 hours. What was his walking rate in miles per hour?

Answers

Answer:

0.6 miles per hours per hour

Step-by-step explanation:

Simply divide 5 by 8

your answer: 0.6 miles per hour.

What dose No mean in math

Answers

Answer:

Nobelium

Step-by-step explanation:

That looks like a chemistry element unless No is meaning the abbreviation No. - Meaning, number.

Ocsar and his little brother made up a game using coins. They flip the coin towards a cup and receive points for every one that makes it in. Oscar starts with 20 points, and his little brother starts with 18 points. Oscar gets 2 points for every successful shot, and his brother, since he is younger, gets 3 points for each successful shot. Eventually, the brother will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have? mar​

Answers

Answer:

Each brother will need 2 additional shots!

Step-by-step explanation:

If you add 3 to 18 it'll eventually lead to 24, as for 2 plus 20, if you add that up it also gets you to 24 which will make the game tied. And the tied score is 24.

The brothers will have a tied score in the game if both brothers are added with two more shots each.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

The points started by Oscar was 20.

The points started by Oscars little brother was 18.

Oscar gets 2 points for every successful shot,

his brother, since he is younger, gets 3 points for each successful shot

If Oscar done 2 more shots his points will be 24.

If Oscars little brother two shots his points will be increased by 6 and will become 24. The brother will have a tied score in the game.

Hence, Each brother will need 2 additional shots

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Here are the boiling points of certain elements in degrees Celsius: Argon: -185.8 Chlorine: -34 Fluorine: -188.1 Hydrogen: -252.87 Krypton: -153.2 Helium: -268.9 Select all the boiling points that are above the boiling point of Argon.

Answers

Answer:

Chlorine: -34 °C

Krypton: -153.2 °C

Step-by-step explanation:

Boiling point of elements in degree Celsius (°C)

Argon: -185.8 °C

Chlorine: -34 °C

Fluorine: -188.1 °C

Hydrogen: -252.87 °C

Krypton: -153.2 °C

Helium: -268.9 °C

Boiling points that are above the boiling point of Argon.

Chlorine: -34 °C

Krypton: -153.2 °C

Paula wants to buy 3 shirts and 2 belts. The shirts cost $16.89 each, and the belts cost $8.97 each. Paula has $45.


Which of these amounts is the best estimate of how much more money Paula needs in order to buy the shirts and belts?


$16

$10

$24

$5

Answers

Answer:

23.61 which rounds to 24

Step-by-step explanation:

3 shirts is 16.89 x 3 which is $50.67

2 belts is 8.97 x 2 = 17.94

68.61

then she already has 45 so subtract

In trapezoid JKLM, determine LM.

Answers

Answer:

LM = 12.1

Step-by-step explanation:

Trapezoid

The midsegment (also known as the median or midline) of a trapezoid is the segment that joins the midpoints of the legs.

The midline is parallel to the bases a and b and its length m is equal to the average of the lengths of the bases of the trapezoid:

[tex]\displaystyle m = \frac{a + b}{2}[/tex]

Since JP and PM are congruent and KQ and QL are congruent, PQ is the midline of the trapezoid JKLM.

We are given the midline m=11.4 and one of the bases a=10.7. We can find the other base by solving for b:

b = 2m - a

b = 2*11.4 - 10.7

b = 12.1

LM = 12.1

consider the inequality x+10 /3>2

highlight which values of x are a solution to the inequality
a. x=-2
b. x=4
c. x=-5
d. x=-20​

Answers

Answer:

a, b

Step-by-step explanation:

-2+10=8÷3=2.66

2.66>2

4+10=14÷3=4.66

4.66>2

-5+10=5÷3=1.66

1.66<2

-20+10=-10÷3=-3.33

-3.33<2

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! REALLLLLLLLLLLY EASY! i'm either dum.b, st.upid, or dum.b

Answers

9514 1404 393

Answer:

  y^6

Step-by-step explanation:

It can help to remember that an exponent is simply an indicator of repeated multiplication. Common factors cancel from numerator and denominator.

  [tex]\dfrac{y^7}{y}=\dfrac{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}{y}=y\cdot y\cdot y\cdot y\cdot y\cdot y=\boxed{y^6}[/tex]

_____

Written as a rule of exponents, this is ...

  (a^b)/(a^c) = a^(b-c)

Of course, a = a^1.

can someone plz help me

Answers

9514 1404 393

Answer:

  C.  168

Step-by-step explanation:

One of the more useful approaches to multiple choice problems is eliminating the answers that don't make any sense.

You know a square has internal angles of 90 degrees, and that polygons with more sides have larger angles. No internal angle can be more than 180 degrees in a regular polygon. The only answer choice in this range is the correct one:

  C.  168

Answer: C.168

Step-by-step explanation:

Your local pizza store sells medium pizzas for $5.69 each, and breadsticks for $2.49 per order.
For a party, you decide to order 4 pizzas and 3 orders of breadsticks. There is a $3 delivery fee, and a 9.4%
sales tax will be added to the total. What will be the total bill after tax?

Answers

Answer:

5.69 X 4 = 22.76

2.49 X 3 = 7.47

22.76 + 7.47 + 3 = 33.23

33.23/100 X 109.4 = 36.35362

monetary unit round to 2dp

$36.35

Answer:

$36.35

Step-by-step explanation:

The area of the rectangle is 27 square feet. Choose the equation you can use to find the value of x. A rectangle. The length is x feet and the width is 3 feet. $3x=27$ $2x+6=48$ $27x=3$

Answers

Answer:

3x = 27

Step-by-step explanation:

Since the area of a rectangle, A = lw where l = length = x and w = width = 3 feet. So, A = 3x. Since A = 27 square feet, 27 = 3x.

So, the required equation is 3x = 27

pls help ill give brainliest if it’s right!!!!!!

Answers

Answer:

Its blurry please take new picture

Step-by-step explanation:

Me ayudan porfass :))

Answers

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

The given triangle is a 30°-60°-90° triangle. Use the following rule:

[tex]hypotenuse=shorter.leg*2[/tex]

We know the length of the hypotenuse, which is 20. Insert the value:

[tex]20=s*2[/tex]

Solve for s. Divide both sides by 2:

[tex]\frac{20}{2} =\frac{s*2}{2} \\\\10=s[/tex]

The length of the shorter leg is 10. Therefore, the value of x is 10.

:Done

¿Cual es la medida del diámetro del circulo unitario? ​

Answers

Answer:

2

Step-by-step explanation:

Un círculo unitario es un círculo con un radio de 1

mercedes got to choose 2 cupcakes, there were 3 chocolate 1 vanilla and 4 carrot cake what is the probability that she will choose vanilla followed by a carrot cupcake without the replacing?

Answers

Answer:

3/64

Step-by-step explanation:

Mercedes has to choose 2 cupcakes.

Given that;

3 : chocolate

1  : vanilla

4 :carrot cake

The probability that she will choose vanilla followed by a carrot cupcake without replacing will be;

Form a tree diagram for two picks

1/8 * 3/8  = 3/64

HELP ASAP Which equation matches the following situation: A shirt, x, is discounted 20%; what is the sale price?

y = 1.02x
y = (1 - 0.2)x
y = 1.2x
y = 0.02x

Answers

Answer:

D

Step-by-step explanation:

k(l - p) + j = s + w solve for P

Answers

9514 1404 393

Answer:

  p = l -(s +w -j)/k

Step-by-step explanation:

We can undo what is done to p.

  [tex]k(l -p)+j=s+w\\\\ k(l-p)=s+w-j \qquad\text{subtract $j$}\\\\ l-p=\dfrac{s+w-j}{k} \qquad\text{divide by $k$}\\\\ l=\dfrac{s+w-j}{k}+p \qquad\text{add $p$}\\\\ \boxed{p=l-\dfrac{s+w-j}{k}} \qquad\text{subtract the fraction}[/tex]

Please Help! A new dirt bike valued at $9000 loses 18% of its value each year. What is the initial price of the dirt bike? I don't understand how to solve this problem so if someone could show me how it would mean a lot.

Answers

Answer:

The new dirt bike should cost $9000

Answer two questions about Systems A and B:
System A
5x +y = 3
4x – 7y = 8
System B
5x+y=3
x+8y=-5
1) How can we get System B from System A?


Answers

Answer: Answer is D and Yes

Step-by-step explanation:

Answer:

add teh add57

Step-by-step explanation:

tyen i how muchho

What is 32,000 divided by 8

Answers

Answer:

Is 4000 the answer is 4000.the answer is 4000

What is the value of x when f(x) = -6. Explain how to find it.
X
-6
у
-12
-6
-3
0
0
3
6
6
12

Answers

Answer:

The function g(x) simply takes the value x and turns it into its reciprocal value . Thus, for instance, the number 5 becomes , and  becomes 2. Note that any value of x works in this function as long as  is defined. As mentioned, fractions work as well as whole numbers, both for positive and negative values; the only value that does not work is 0, since  is undefined (how many times can 0 go into 1?). Thus, the domain of the function is all x in  where x ≠ 0. Let's look at the graph of the function also.

Step-by-step explanation:

The function f simply takes in input value x, multiplies it by 2, and then adds 3 to the result. We can therefore consider what constitutes the set of numbers that the function can accept as an input and what constitutes the set of numbers that the function can yield as an output.

what is the slope of the line?? help!

Answers

Answer: 1/3

Step-by-step explanation:

The answer is

y = -1/3x + 2/3

need help please also watch Attack on Titan
Levi

Answers

Answer:

B.

Step-by-step explanation:

The sets represented is {50,70,70,75,75,95,95,100}

The Kid Laroi

Answer:

The answer is B

Step-by-step explanation:

Levi is mine

if you were planning a meal for 24 people, how many dozens eggs would you need to buy if each person were to have 2 eggs each

Answers

Answer:

4

Step-by-step explanation:

If each person has 2 eggs, you'd need 48, and since a dozen is 12, 12*4=48.

Answer:

4 dozen eggs

Step-by-step explanation:

12 is a dozen and 12+12=24.

So you would need 4 dozen eggs to give each person 2 eggs.

What is one half ( 1/2 ) squared?

Answers

Answer:

[tex](\frac{1}{2} )^{2} =\frac{1^2}{2^2} = \frac{1} {4}}[/tex]

When squaring a fraction, square both numerator AND denominator

The answer is 1/4
1/2x1/2=1/4

find the y-intercept for the equation y=15x-3

Answers

Answer:

(0,-3)

Step-by-step explanation:

the y intercept is the last number of the expression; in this case it's negative 3. x is always 0

8th grade Pythagorean Theorem Work need this done in under 2 minutes ASAP this is a grade and I do not wanna fail !!!!!

Answers

Answer:

202 meters

Step-by-step explanation:

can someone help me with this question, ill give brainiest.

Answers

44s = the product of 44 and s.

44s = 44 × s

If we multiply a number with a variable we would get for example

22 × a would be 22a

10 × u = 10u

Help! I’m taking a test and don’t get this Solve x/4-2=2

Answers

Answer:

x is 16

Step-by-step explanation:

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