Mathematics Middle School

1. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
(Please show me how you get your answers)
I nEED HELP!

Answers

Answer 1
Let us divide the shape of the cake into two parts:

1) The cylindrical part.
2) The cone of the tent.

Note: In order to find the total volume of the cake, we have to add the volumes of both of the above-mentioned part.


1.
The volume of the cylinder = [tex] \pi *r^{2}*h[/tex] --- (A)

We have the height = h = 14 inches.
Radius = r = Diameter / 2 = 12/2 = 6 inches.

and [tex]\pi [/tex]= 3.14

Put the above values in equation (A);
(A) => The volume of the cylinder = (3.14) * (6 x 6) * (14) = 1582.56 inches cubed

2. 
The volume of the cone = [tex]\pi *r^{2}* \frac{h}{3} [/tex] --- (B)

Since the cake is in "circus tent" shape, therefore, the radius of the cone should be equal to the radius of the cylinder.

Radius of the cone = r = 6 inches.
Height of the cone = h = 6 inches.

and [tex]\pi [/tex]= 3.14

Put the above values in equation (B);
(B) => The volume of the cone = (3.14) * (6 x 6) * (6 / 3) = 226.08 inches cubed

The volume of the cake = Volume of the cylinder + Volume of the cone
[tex]V_{cake}[/tex]  = 1582.56 + 226.08 = 1808.64 inches cubed

Ans: The volume of the cake = 1808.64 [tex]in^{3}[/tex]

-i

Related Questions

Which percents would be close to 7%? 4.8% 5.2%. 6.8%. 5.5%

Answers

6.8% because when you round it up, it would equal 7%

The Lee’s spend $31 on movies tickets for 2 adult and 3 children. The Smith’s spent $26 on movie tickets for 2 adults and 2 children. What are the prices for an adult and child movie ticket?

Answers

First we write the variables:
 x: cost of the ticket for adults.
 y: cost of ticket for children.
 We write the system of equations:
 2x + 3y = 31
 2x + 2y = 26
 We solve the system:
 Step 1:
 2x + 3y = 31
 -2x-2y = -26
 Step 2:
 y = 5
 Step 3:
 2x + 3y = 31
 2x = -3y + 31
 x = (- 3y + 31) / 2
 x = (- 3 * (5) +31) / 2
 x = 8
 Answer:
 the prices for an adult and child movie ticket are:
 adults = $ 8
 children = 5 $

How many units are between (9,6) and (-16,6)?

Answers

[tex]d= \sqrt{(9-(-16))^2+(6-6)^2}= \sqrt{25^2}=25 [/tex]

25 units

Jasmine has 50 shares of a stock. The value of each share went down by $2 today. Express the total change in value of Jasmines shares as an integer calculation.

Answers

The change is Jasmine's stock is represented by -$100.

If each stock dropped by a value of $2 and she had 50 stocks, she had a 50 x $2 change. Because The stock dropped this is a negative change.
Answer:
The rate of change would, be -$100 where the negative sign expresses a decrease in the value of total share.

Explanation:
We are given that:
Jasmine has 50 shares
Value of each share decreased by $2

This means that:
Jasmine's total shares decreased by 50*2 = $100

The rate of change would, thus, be -$100 where the negative sign expresses a decrease.

Hope this helps :)

What is the area of this figure ?

Answers

 Remember that what you must do for this case is to calculate the area of the parallelogram and add it to the area of the rectangle.
  Palelogram area:
  Knowing the base and the height, the area of the parallelogram is calculated by its formula: 
  A1 = b * h
  We have then
  b = root ((- 4 - (- 10)) ^ 2+ (2-2) ^ 2) = 6
  h = root ((- 7 - (- 7)) ^ 2+ (3-2) ^ 2) = 1
  A1 = (6) * (1) = 6 units ^ 2
  Rectangle area
  A2 = L * W
   We have then:
  L = root ((1 - (- 2)) ^ 2 + (- 3 - (- 4)) ^ 2) = 3.16227766
  W = root ((- 4 - (- 2)) ^ 2+ (2 - (- 4)) ^ 2) = 6.32455532
  A2 = (3.16227766) * (6.32455532)
  A2 = 20 units ^ 2
  The total area is the sum of both ares:
  A = A1 + A2
  A = 6 + 20
  A = 26 units ^ 2
  Answer:
  the area of this figure
  A = 26 units ^ 2


A ladder is placed 7 feet from the base of a building and reaches a point on the building that is 24 feet above the ground.Find the length of the ladder?

Answers

◆ Pythagoras Theoram ◆

Hey !!

Check the attachment.
Hope it helps you :)

The length of the hypotenuse or the ladder is 25 feet.

What is a triangle?

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A ladder is placed 7 feet from the base of a building and reaches a point on the building that is 24 feet above the ground.

So, The base is 7 feet and the height is 24 feet.

Therefore,

Hypotenuse² = Base² + Height².

Hypotenuse = [tex]\sqrt{49 + 576}[/tex].

Hypotenuse = [tex]\sqrt{625}[/tex].

Hypotenuse = 25 feet.

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Richard caught f fish two weeks ago and 32 fish last week.
How many fish has Richard caught these last two weeks combined?
Write your answer as an expression.

Answers

Answer:

The answer is f+32

Step-by-step explanation:


The expression which represents the total fish caught by Richard is

f + 32.

What is expression?

A set of variables, constants, and mathematical operations forms an algebraic expression.

According to the given question.

The number of fishes caught by Richard two weeks ago = f

And the fish caught by Richard last week = 32

Therefore,

The expression for the total fish caught by Richard these last two weeks

= f + 32

Hence, the expression which represents the total fish caught by Richard is f + 32.

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Find the area to the right of a z score of 2.75 under a standard normal distribution curve

Answers

It is about 0.298% as calculated by my TI-83/84 work-alike.

last summer Marion was three and a half feet tall she was 4 inches taller than her brother Elijah she was one in a quarter feet shorter than her sister Lori how tall were Elijah and Lori Last Summer

Answers

Let M be Marion, L be Lori and E be Elijah.
M = 3.5 ft.
E = M - 4/12 (since he was 4 inches shorter than Marion) = 3 1/2 - 4/12; find a common denominator (12):  3 6/12 - 4/12 = 3 2/12 = 3 1/6 ft.
L = M + 1.25 (since she was 1 1/4 feet taller than Marion) = 3.5 + 1.25 = 4.75 feet.

A right rectangular prism has a length of 6 inches, a width of 9 inches, and a height of 10 inches. What is the surface area of the prism? Enter your answer in the box. in²

Answers

the
Answer=408in2
hoped i helped




Answer:

A=408in²

Step-by-step explanation:

A=2(wl+hl+hw)=2·(9·6+10·6+10·9)=408in²

Three girls collected geodes in the desert. Corinne collected 11 1/8 pounds, Ellen collected 4 5/8 pounds, and Leonda collected 3 3/4 pounds. How much did Corinne collected than the other two girls?

Answers

Corinne collected 2 3/4 pounds more than Ellen and Leonda's collection combined. Here is the work that I did to get the answer (Red represents my work while highlighter represents the answer):

Answer:

2 3/4

Step-by-step explanation:

To build a desktop you put 2 boards together . One board is 1/3 inch thick, and the other is 1/2 inch thick . How thick will the desktop be?

Answers

The answer is 5/6 inches thick

How many different triangles can be constructed with three angles, each measuring 30°?

Answers

Okay to have a complete triangle with 3 angles  it must add up to 180° So therefore if you have  30° For each angle  which adds up too 90°. We're are still missing 90 more degrees. So that means we can't  make a triangle at all.

Kaylie had $1250 in her saving account. She withdrew $82 each month in order to pay for a summer vacation. How much did Kaylie have in he account at the end of eight months?

Answers

$594 would be your answer :)

what is between 3/8 in a number line

Answers

Okay I hope this is what you mean. so if you are saying what is between the numbers 3 and 8 we can make an inequality which will cover all the small decimals between the numbers.

There are 2 different equalities that I'm not sure which one you want.

so the first one would be
[tex]3 \leqslant x \leqslant 8[/tex]
x is just the variable I chose for this. Now this inequality means that both 3 and 8 are solutions to the problem. x represent all the little numbers in between so to test your answers just plugin the number you're testing in for x. Since 3 is the lowest number it will have a less than or equal to (in this case) sign and 8 is the greatest so that's why the open/greater side is facing the 8. It reads 3 is less than or equal to x and x is less than or equal to 8.

If you meant all number in between 3 and 8 not include either of those numbers than the inequality would be
[tex]3 < x < 8[/tex]
In this case all the numbers between 3 and 8 are solutions but 3 and 8 will not be solutions. the line under the symbol means it includes the number which come before or after it. The inequality reads 3 is less than x which is less than 8. You can also plugin in an answer to test it in place of x.


If you have any questions or it turns out you meant somthing else please tell me and I'll be happy to help, sorry if this isn't what you meant in the question.

mathew is 2 yards tall how many inches tall is he.

Answers

he 72 inches tall because a yard is 36 inches and 36 times 2 is 72 
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Hey there!


The answer is : 72 inches 
Reason: a yard is 3 ft and a foot is 12 in so ,
1 yard is 36 in and 2 yards is 72 in


Hopes this Helps u :D

What is the y intercept of y = 6x + 32?

Question 4 options:

6


6x


32


0

Answers

To find out the y-intercept of a function, we fill in x = 0

This gives us the following:
y = 6 * 0 + 32 = 0 + 32 = 32

So, the y-intercept is 32.
Final answer:

The y-intercept of y = 6x + 32 is 32.

Explanation:

The y-intercept of a linear equation is the point where the graph of the equation intersects the y-axis. In the equation y = 6x + 32, the y-intercept is the value of y when x is equal to 0. To find it, substitute 0 for x in the equation: y = 6(0) + 32. Simplify the equation to find that the y-intercept is 32.

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A bear cub weighed 64 oz in March. After three months, it weighed 31 lbs. How many lbs did the cub weigh in March?

Answers

it weight 33 oz in march



4 lbs
64 oz is 4 lbs

Kit bought a soft drink and a sandwich for $9.00. What was the price of each if the sandwich cost 3.5 times much as the soft drink?

Answers

Let the cost of the soft drink = C   then the price of the sandwich was 3.5 times as much = 3.5C

 

And

 

C + 3.5C  = Total Cost

 

C + 3.5C  =   9

 

4.5C = 9    divide both sides by 4.5

 

C = 9/4.5  =  $2.00   for the soft drink

 

And  3.5C = 3.5(2.00)  = $7.00   cost of the sandwich

If Kit bought a soft drink and a sandwich for $9.00 and the sandwich cost 3.5 times much as the soft drink the price of the sandwich and soft drinks will be $7.00 and $2.00 respectively.

What are arithmetic operations?

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that, Kit spent $9.00 on a soft drink and a sandwich, with the food being 3.5 times as expensive as the soft drink.

Suppose the cost of the soft drink is x as a result the price of the sandwich will be 3.5x.

Total cost = $9

x+3.5x=9

4.5x=9

x=9/4.5  

x=  $2.00

The price of the sandwich obtained as,

=3.5x

=3.5× $2.00

=$7

Thus, if Kit bought a soft drink and a sandwich for $9.00 and the sandwich cost 3.5 times much as the soft drink the price of the sandwich and soft drinks will be $7.00 and $2.00 respectively.

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The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to disintegrate. Suppose you started with 200 grams of a substance with a half-life of 3 minutes. How many minutes have passed if 25 grams now remain? Explain your reasoning.

Answers

3 half-lives because 200/2=100 100/2=50 and 50/2=25 

Answer:

It would take 9 minutes for 25 grams of the substance to remain.

Step-by-step explanation:

Radioactive substance degenerate to release particles and lot of energy. The time required for a radioactive substance to degenerate into half of its original size is termed half life. The substance continues the stages of degeneration with respect to the half life.

The given substance would have 3 stages of degeneration to achieve a mass of 25 grams with respect to the half life.

1st stage, it would degenerate to half of its original size;

          = [tex]\frac{200}{2}[/tex]

          = 100 grams

This occurs in 3 minutes.

2nd stage, it would degenerate to half of its previous size;

        = [tex]\frac{100}{2}[/tex]

       = 50 grams

This also occurs in 3 minutes.

3rd stage, it would degenerate to half of it previous size;

         = [tex]\frac{50}{2}[/tex]

        = 25 grams

This also occurs in 3 minutes.

We stop here due to the restriction in the question for 25 grams.

So, the total time taken for the substance to reach a mass of 25 grams

       = 3 + 3 + 3

       = 9 minutes

It would take 9 minutes for 25 grams of the substance to remain.

Help help help plz give me the right answer

Answers

L = large
M = Medium
S = Small

L = 3*s
M = 2*s

L + S = 2940
Substitute 3s for L
3s + s = 2940
4s = 2940
s = 2940/4
s = 735

M = 2*S
M = 2* 735 
M = 1470

L = 3*S
L = 3*735
L = 2205

You should check this
L + M + S =? 2940
2205   + 735 = 2940 which checks that much of it.

)The table below shows a correct representation that 16 pounds (lb) of sugar cost $4: lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1 $1
true or faulse?

Answers

If 16 pounds (lb) of sugar cost $4, then the cost per pound would be

  $4          
---------- = $0.25 / lb (answer)
 16 lb

Answer:

it is true

Step-by-step explanation:

What is the value of x in this number sentence?


32 = 17 + x


Answers

32 = 17 + x
32 - 17 = x
15 = x
32  = 17 + x
To find our answer, the value of x, we only have to substract 17 from both sides. This gives us the following
15 = x
x = 15
So the value of x in this number sentence is 15

What is the greatest amount of cups of green ooze any one contestant carried?

Answers

Hey there. In the comments above, let's list these fractions and convert them into decimals for a more simple comprehension level:
0; 1/8; 3/8; 1/2; 5/8; 3/4; 7/8; and 1. The converted list below will correspond with these fractions in order:
0; 0.125; 0.375; 0.5; 0.625; 0.75; 0.875; and 1.00.

Looking at these decimals, 1.00 is the greatest amount as it is the only fraction that converted to a whole number.

I hope this helps!
The fraction with the greatest amount is 1 as it is 1 whole. Therefore makeing it he largest!

In order from greatest to least:

1.

7/8 ; 0.875

3/4 ; 0.75

1/2 ; 0.5

5/8 ; 0.625

1/4 ; 0.25

3/8 ; 0.375

1/8 ; 0.125

0.

I hope this helps!
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Have a wonderful day! : )

What is 6x – 8 = 4 written as a system?

A. y = 6x – 8
y = –4

B. y = 6x – 8
y = 4

C. y = –6x + 8
y = 4

Answers

Answer:
y = 6x - 8
y = 4
which is the second option

Explanation:
The general form of a linear system is:
y = mx + c
The given equation is:
4 = 6x - 8

Comparing the given equation with the general form, we will find that:
The system is:
y = 6x - 8
y = 4

Hope this helps :)

6x – 8 = 4 written as a system y = 6x – 8, y = 4. So, option B) is correct.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given,

6x-8=4

For A) Given system

y = 6x – 8.....................1

y = –4.....................2

Substituting y=-4 in eq 1

-4=6x – 8

6x – 8=-4, which is not the same as the given equation.

For B) Given system

y = 6x – 8.....................3

y = 4.....................4

Substituting y=4 in eq 3

4=6x – 8

6x – 8=4, which is the same as the given equation.

For C) Given system

y = -6x +8.....................5

y = 4.....................6

Substituting y=4 in eq 5

4=-6x + 8

-6x +8=4, which is the same as the given equation.

Thus,  6x – 8 = 4 written as a system  y = 6x – 8, y = 4. So, option B) is correct.

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What is the range of the function represented by the table?
A {2, 4, 6, 8, 10}

B {2.5, 5.0, 7.5, 10.0, 12.5}

C {2, 2.5, 4, 5.0, 6, 7.5, 8, 10, 12.5}

D {0.0, 0.5}

Answers

Answer:

{2.5, 5.0, 7.5, 10.0, 12.5}

Step-by-step explanation:

4n-3=-2n+9 What is the value of the variable 'n'?

Answers

4n - 3= -2n + 9
add 3n to both sides

4n= -2n +12
add 2n to both sides

6n= 12
divide both sides by 6

n= 2

Check:
4n-3=-2n+9
4(2)-3= -2(2)+9
8-3= -4+9
5=5


Hope this helps! :)

He height of a triangle is 9 m less than is base the area is 56 m^2 what is the length of the base?

Answers

Formula for area of triangle:
A= 1/2 bh
Where b is the base and h is the height of the triangle.
Here, h= b-9
A=56 m^2
Put values in formula.
56= 1/2 (b) (b-9)
56=b(b-9)/2
Multiply both sides by 2.
112=b^2-9b
or
b^2-9b-112=0
Factorise the equation.
b^2-16b+7b-112=0
b(b-16)+7(b-16)=0
(b+7)(b-16)=0
Using zero factor theorem.
b+7=0 or b=-7
and
b-16=0 or b=16
Ignore the value b=-7, because length cannot be negative.
So length of base=16 m

Answer: Base=16m


In which quadrant is the point (0,7) located? Explain your answer.

Answers

0, 7 is placed in the top middle quadrant because the x value is 0, therefore it does not move left or right, and y is placed up into the middle. Mark Branliest. :-)

Melanie eats 1.5 pounds of cereal each week. Which model below best represents the number of pounds of cereal she eats in .5 weeks?

Answers

For this case, the first thing we must do is define a variable.
 We have then:
 x: number of weeks
 y: amount of cereal that Melanie eats
 We now write the function that models the problem:
 [tex]y = 1.5x [/tex]
 Then, for 5 weeks we have:
 [tex]y = 1.5 (5) y = 7.5 pounds[/tex]
 Answer:
 A model that best represents the number of pounds of cereal she eats is:
 [tex]y = 1.5x [/tex]
 For 5 weeks we have:
 [tex]y = 7.5 pounds[/tex]
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