A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it? (Please explain and show work)
Answers
=================================================
Work Shown:
A = volume of the cylinder
A = pi*(radius)^2*(height)
A = pi*r^2*h
-----------
The cone's base has diameter r/2, so its radius is (1/2)*(r/2) = r/4
B = volume of the cone
B = (1/3)*(volume of cylinder with radius r/4 and height h)
B = (1/3)pi*(r/4)^2*h
B = (1/3)*pi*(r^2)/(4^2)*h
B = (1/3)*pi*(r^2)/16*h
B = (1/3)*(1/16)*pi*r^2*h
B = (1/48)pi*r^2*h
B = (1/48)*A
B = (1/48)*(volume of cylinder)
-----------
C = volume of the empty space/air inside cylinder, but outside cone
C = A-B
C = A - (1/48)*A
C = (48/48)A - (1/48)A
C = (48A)/48 - (A/48)
C = (48A-A)/48
C = 47A/48
C = (47/48)*A
C = (47/48)*pi*r^2*h
Related Questions
Which coordinate notation matches the description?:
3 units left and 5 units down
O (x+3y-5)
O (X-3.y-5)
O (x+3.y+5)
O (X-3.y+5)
Answers
Answer: The last one
Step-by-step explanation:
3 units left would be -3 and 5 units down would be +5
-3(2t - 1) = t + t + t + 3
Answers
isolate the variable
Answer:
-3(2t - 1) = t + t + t + 3
-6t + 3 = 3t + 3
-6t -3t = 3t - 3t +3
-9t + 3 - 3 = 0
9t = 0
t = 0
Step-by-step explanation:
2/5 x 1 2/3
i know its easy
Answers
Answer:
2/3
Step-by-step explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
25×53
Applying the fractions formula for multiplication,
=2×55×3
=10/15
Simplifying 10/15, the answer is
=2/3
What’s the volume of this shape?
Answers
Answer:
V=72x³y³
Step-by-step explanation:
The formula to apply is;
V= l * w * h where
V= volume in units cubed.
l= length = 3xy
w=width = 4xy
h= height = 6xy
Substitute values in the formula as;
V= l*w*h
V=3xy * 4xy * 6xy ----find product for the numbers {3*4*6=72} then multiply by the product for x's {x*x*x =x³} that of y's {y*y*y=y³}
V= 72*x³*y³
V= 72x³y³ --------where xy are the units used.
The quotient of –125 and 5 is
.
The quotient of –264 and –12 is
.
The quotient of 0 and –350 is
.
The quotient of 276 and –8 is
.
Answers
Answer:
1= -25
2= 22
3= 0
4= -34.5
Answer:
1 negative
2 positive
3 zero
4 negative
Step-by-step explanation:
Hope this helps :D
3x² + 22x + 35
Factor the trinomial
Help guys asp!!
Answers
Answer:
(x + 5)(3x + 7)
Step-by-step explanation:
Given
3x² + 22x + 35
Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term
product = 3 × 35 = 105 and sum = 22
The factors are + 15 and + 7
Use these factors to split the x- term
= 3x² + 15x + 7x + 35 ( factor the first/second and third/fourth terms )
= 3x(x + 5) + 7(x + 5) ← factor out (x + 5) from each term
= (x + 5)(3x + 7) ← in factored form
Help me please...............
Answers
Answer:
Search it up
Step-by-step explanation:
GO ON GOOGLE sorry i couldnt help :(
if medain of 10, 20, x+5,x+10,50,60 is 35 then find x
Answers
Answer:
X = 27
Step-by-step explanation:
10, 20, 32, 37, 50, 60
First things first, take off 10, 20, 50, and 60.
Now, you remain with 32 and 37. Now from here it is simple.
Average of 32 and 37 = 34.83
Round 34.83 to 35
32 averaging 37 (Rounding Terms) ≈ 35
So X is 27
A restaurant coffee pot holds 3 gallons of coffee. The pot has been filled with 2 gallons of coffee. If the variable c stands for the amount of additional coffee the pot can hold, which of the following units could apply to that variable?
A. yards
B. pounds
C. gallons
D. bushels
Answers
C
Because your weight system is gallons in the rest of the question :)
Answer:
gallons
Step-by-step explanation:
Jeremy is saving up to buy a new video game system. Two weeks ago, Jeremy only had $14.75. He has worked for 26 hours at the local grocery store, where he earns $10.15 per hour. If the video game system costs $400.00, how many more hours must Jeremy work before he can purchase the system?
Answers
Answer:
12 more hours
Step-by-step explanation:
$400 is the cost (LESS) $14.75 that he has already
Total needed is now $385.25
He worked 26 hours at 10.15 = $263.90 that he already has
$385.25-$263.90 = $121.35
$121.35 Divided by his hourly wage of $10.15 = 11.95 (or 12 hours)
7 to the 3rd power as a multiplication of factors is
Answers
Answer:
7*7*7
Step-by-step explanation:
7^3=7*7*7
hope this helps
Answer:
7×7×7= 343
Step-by-step explanation:
the answer is 343.
a product of y2 + 5y + 4?
Answers
Answer:
(y + 4)(y + 1)
Step-by-step explanation:
Given
y² + 5y + 4
Consider the factors of the constant term (+ 4) which sum to give the coefficient of the y- term (+ 5)
The factors are + 4 and + 1 , since
4 × 1 = 4 and sum = 4 + 1 = 5 , thus
y² + 5y + 4 = (y + 4)(y + 1) ← as a product of factors
EMERGENCY! Please give me the correct answer!
Answers
Answer: 10^4 · 4^5
Since 4^10 and 4^5 have the same base, and it's division, you can subtract the exponents.
(10^4 · 4^10)/4^5 = 10^4 · 4^(10-5) = 10^4 · 4^5
Which number is rational, an integer, and a real number?
A. 1.5
B.
C. There is no such nurnber.
D. -5
Answers
1.5
Explanation:
what is the answer if u do x=25(x+4)
Answers
Answer:
-25 over 6 as a fraction or -4 and 1 over 6 as simplified fraction or 4.16 as a decimal
Step-by-step explanation:
hopefully that helps you
Please solve that problem my homework is due ✨
Answers
Answer:
1,100 miles traveled in 2 hours, 3,300 miles in 6 hours
Step-by-step explanation:
if the plane is moving at a constant speed, to find the miles per hour divide the distance traveled over the time (1650/3). this would get you 550 miles per hour. So, to get the distances at the other times multiply the times by the speed to get distance traveled. (2*550) and (6*550)
Whats the answer to this the domain of the function URGENT!!!!!!!!!!!!!
Answers
Answer:
I think it's d I'm not sure tho
Answer:
B
Step-by-step explanation:
I'm pritty sure it is B hopefully this helps.
For a given recipe, 12 cups of flour are mixed with 24 cups of sugar. How many cups of sugar should be used if 21 cups of flour are used?
Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x. PLEASE ANSWER THIS QUICK
Answers
Answer:
33 cups of sugar should be used
Step-by-step explanation:
subtract 12 from 21 then add that answer to 24 and you get 33 so 33 cups of sugar should be used
42 cups of sugar should be used if 21 cups of flour are used
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
For a given recipe, 12 cups of flour are mixed with 24 cups of sugar
We need to find cups of sugar should be used if 21 cups of flour are used
Let us consider x as cups of sugar should be used if 21 cups of flour are used
Let us form an equation to find x
12/24=21/x
Apply cross multiplication
12x=21×24
12x=504
Divide both sides by 12
x=504/12
x=42
Hence, 42 cups of sugar should be used if 21 cups of flour are used
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ2
A G.P bulk bills at $36.30 per consultation, and sees a new patient every 12 minutes for 3 hours. A new employee calculates the number of patients and then calculates the medicare bills as follows.
Number of patients:3÷ 0.12=25
Medicare bill: 25x$36.30=907.50
(a)identify and describe the error
(b)recalculate the Medicare bill
Answers
Answer:
$544.5
Step-by-step explanation:
a) 12 minutes is 0.2 hours.
So 3/0.2= 15 patients.
b) 15*36.3= $544.5
i mark as brainliest
Answers
Answer:
-6.75
Step-by-step explanation:
Answer:
The answer is D. -7.25
Find the total surface area of this cuboid.
5 cm
4 cm
6 cm
Answers
Answer:
e total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is ... 1: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm. ... Example 2: Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm ... Example 4: The length, breadth and height of a cuboid are 16cm, 14cm and ...
Step-by-step explanation:
Where's the cuboid? You left it out.
In any case, use the following formula:
SA = 2(front + side + top)
Is the statement true or false
Answers
Answer:
it is false
Step-by-step explanation:
-3 is lesser on the number line so remember "The Alligator" wants the higher number :)
David drives 4.8 miles to Musanze and a further 6.7 miles to Gisenyi. Work out how far he drives in total.
Answers
Answer:
11.6 miles
Step-by-step explanation:
Well all u do is add 4.8+6.7=11.5
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Answers
Answer:
D. 75
Step-by-step explanation:
Bc they are congruent that means that DAY has angles 60 and 45 so you add them together to get 105 and bc triangles are 180 deg, the last angle is 75 (180-105 = 75)
4.3602x10^4 estimate
Answers
Answer:34
4
Step-by-step explanation:
Answer:
43602
Step-by-step explanation:
hope this helps :)
m² - 9m +8
(Factoring)
show steps
Answers
Answer:
I really dont know sorry love <3
Step-by-step explanation:
Select the symbol that properly compares each pair of numbers:
a. -|-15| ___ -(-15)
• <
• >
• =
b. |-18| ___ -18
• <
• >
• =
c. -|-3| ___ -|3|
• <
• >
• =
d. -|-6| ___ |-6|
• <
• >
• =
Answers
Answer:
a. >
b.<
c.=
Step-by-step explanation:
It takes 40 units of maple sap to produce 1 ounce of maple syrup. Jane and her family are bottling maple syrup in 20 -ounce bottles. She notices that they leave about 2 ounces of air every time they fill a bottle, to avoid overfill. How much maple sap did they need to collect to fill 15 bottles? How much less maple sap did they need than if they would have filled each bottle to the top? Express your answer as a negative number.
Answers
Answer:
10,800
-1200
Step-by-step explanation:
Given that :
40 units of maple sap = 1 ounce of maple syrup
Using a 20 - ounce bottle, 2 ounces of air is left
Ounces of actual syrup = (20 - 2) = 18 ounces
Number of maple sap required to fill 15 bottles :
Number of maple saps required to fill 18 ounces bottle :
40 units = 1 ounce
x = 18 ounces
Hence, for 18 ounces of maple syrup :
(40 * 18).= 720 units of maple sap
For 15 bottles of 18 ounces maple syrup:
(720 * 15) = 10,800 units of maple sap
If they had filled each bottle to the top:
(40 * 20 * 15) = 12000 units of maple sap
10,800 - 12000 = - 1200 units of maple sap
what's 4 divided by 5 as a fraction
Answers
Answer:
four fifths because if you divided 4 by 5 is 0.8 and that equals four fifths
Which point is a solution to ys 4x + 5?
O A. (0,10
O B. (-6,4)
O C. (-4,0)
O D. (0-2)
Answers
you plug in x and y which gives you -2 < 0+5
next, you add the two numbers in the right side and get 5
the final product should be -2 < 5 ( 2 is less than 5) which is true
hope this helps :)