A cone has twice the base diameter and three-fourths the height of a cylinder. Can you tell what the relationship between the volume of the cone and the volume of the cylinder is? Explain your reasoning.
Answer:
Equal volumes
Step-by-step explanation:
Given
[tex]h \to[/tex] height of cone
[tex]d \to[/tex] diameter of cone
[tex]H \to[/tex] height of cylinder
[tex]D \to[/tex] diameter of cylinder
Such that:
[tex]d = 2D[/tex]
[tex]h =\frac{3}{4}H[/tex]
Required
The relationship between the volumes
The volume of a cylinder is:
[tex]V_1 = \pi R^2H[/tex]
Where
[tex]R = 0.5D[/tex]
So:
[tex]V_1 = \pi (0.5D)^2H[/tex]
[tex]V_1 = \pi *0.25*D^2H[/tex]
[tex]V_1 = 0.25\pi D^2H[/tex]
The volume of the cone is:
[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]
Where
[tex]r =0.5d[/tex]
[tex]r = 0.5 * 2D[/tex]
[tex]r = D[/tex]
and
[tex]h =\frac{3}{4}H[/tex]
So, we have:
[tex]V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H[/tex]
[tex]V_2 = \frac{1}{4}\pi * D^2H[/tex]
[tex]V_2 = 0.25\pi * D^2H[/tex]
[tex]V_2 = 0.25\pi D^2H[/tex]
So, we have:
[tex]V_1 = 0.25\pi D^2H[/tex]
[tex]V_2 = 0.25\pi * D^2H[/tex]
[tex]V_1 = V_2[/tex]
Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.
Step-by-step explanation:
Philip bought a pair of jeans that were on sale. The jeans cost $45 before the sale. The sale discount was $9.
Which percent shows the discount Philip got on his jeans?
Answer: It’s 5%
Step-by-step explanation:45 divided by 9 is 5 so that the answer :)
Perform the following calculations. To calculate the number of pounds of meat required to feed diners do the following: for poultry or meat with bones, divide the number to be served by 2.5; for meat with little or no bone, divide the number to be served by 3.5; and for fish fillets divide the number to be served by 3.5. Guests = 100 Meat served = boneless chicken How many pounds of chicken are required?
Answer:
28.58 pounds, about 29 pounds
Step-by-step explanation:
Poultry meat with bones ; divide number to be served by 2.5
Meat with little or no bone ; divide number to be served by 3.5
If number of guests to be served = 100
Meat served = 100
The number of pounds of chicken required :
Number of guests to be served / meat served
Hence,
100 / 3.5
= 28.58 ; which is about 29 pounds
Answer:
43
Step-by-step explanation:
If SW ⊥ RT, m< RSU = 5x+17, and m<VST = 9x-11, find m<WSV.
Answer:
uhhhh.....wut?
Step-by-step explanation:
The measure of the angle WSV is 38 degrees.
What is the complementry angles?Complementary Angles Two angles are Complementary when they add up to 90 degrees.
The value of x is;
[tex]\rm 5x+17=9x-11\\\\ 5x-9x=-11-17\\\\-4x=-28\\\\x =\dfrac{-28}{-4}\\\\x=7[/tex]
The angle VST is equlas to;
[tex]\angle \rm VST=9x-11=9(7)-11=63-11=52 \ degrees[/tex]
The angle VST and angle WSV are the complementary angles;
[tex]\angle \rm WSV+\angle VST=90\\\\\angle \rm WSV+52=90\\\\ \angle \rm WSV=90-52\\\\\angle \rm WSV=38[/tex]
Hence, the measure of the angle WSV is 38 degrees.
Learn more about complementry angles here;
https://brainly.com/question/18482336
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Which of the following fraction is the largest ?
5/6
7/12
4/7
2/3
Answer:
5/6
Step-by-step explanation:
So to do this, lets convert all of these fractions into decimals by dividing:
5/6 --> 0.833...
7/12 --> 0.583...
4/7 --> 0.571...
2/3 --> 0.66...
From this, it can be see that it is 5/6, since it is a larger decimal compared to the other choices.
I reposted this someone gave me a link and it tried to give me a virus
Answer:
216 cubic centimeters
Step-by-step explanation:
I divided the shape as two separate rectangular prisms.
4 times 6 times 6 = 144
3 times 4 times 6 = 72
144 + 72 = 216
I hope this helps! :-)
What does x and y equal
Find the sum of the given geometric series: n = 8, r = 3, a = 1/2
Answer:
a⁸=112 is the answer.
Step-by-step explanation:
a⁸=32(1/2)⁷
a⁸=32(7/2)
a⁸=112
I need help with this question hurry
Answer:
a b c and f
Step-by-step explanation:
rectangle parallelogram square and rhombus
15 pts, Solve a right triangle. Please write your answers as it says on the mandate, Thanks!
Hence,
Hence, EG = 5√2And, FG = 5√6Hope it helps you. Please don't mind my rude handwriting. Just pretend it get bent due to a cyclone.
Someone helppp!!!!!!
The two line plots below show the number of hours per week students in Mr. Pinkos' class spend doing homework and watching television
Answer:
Step-by-step explanation:
I need help
Solve each log equation for real solutionslogx 81 =2
Answer:
x=9
Step-by-step explanation:
You would change it to x^2 = 81 which is 9.
NEED ANSWERS!!!!!!!!!!
Answer:
(1,0) and (3,0)
Step-by-step explanation:
The roots are always shown where the parabola crosses the x-axis.
In this particular graph, the parabola crosses at (1, 0) and (3, 0). Which means the roots are:
x = 1 and x = 3
Hi, I need help pretty please! (This time with 5 screenshots)
Acabcompanycharges $ 4 percabride,plusanadditional $ 1 permiledriven.Howlongisacabridethatcosts $ 28 ?
Answer:
24 miles
Step-by-step explanation:
Given that the cost of the company consist of two elements; a fixed cost equivalent to $4 and a variable cost element which depends on the miles driven. If the car travels x miles then the cost will be
= 4 + 1*x
= 4 + x
If the total cost is $28 then
4 + x = 28
Subtract 4 from both sides
x = 28 - 4
= 24
The car ride is
24/1 = 24 miles
2 t-shirts and 3 hats costs £12.
5 t-shirts and 4 hats costs £23.
Find the cost of a t-shirt.
Find the cost of a hat.
The cost of a t-shirt is £3 and the cost of a hat is £2.
What is a linear equation?
When an equation contains one or more variables with exponents as 1 then such equations are linear equations.
For example, 3x+2y=9 and 4y=6. The first equation is a linear equation with two variables and the second equation is with the linear equation in one variable.
Let the cost of a t-shirt is £m and the cost of a hat is £n.
Formulate two linear equations using the given statements in the question.
[tex]2m+3n=12\,\,\, ...(1)\\5m+4n=23\,\,\, ...(2)[/tex]
Obtain the value of m from equation (1).
[tex]2m=12-3n\\m=\frac{12-3n}{2}[/tex]
Substitute the obtained value of m into equation (1) and find n.
[tex]5 \times(\frac{12-3n}{2})+4n=23\\ 60-15n+8n=46\\14=7n\\n=2[/tex]
Substitute the value of n into [tex]m=\frac{12-3n}{2}[/tex]and obtain the value of m.
[tex]m=\frac{12-3(2)}{2}\\=\frac{12-6}{2}\\ =\frac{6}{2}\\ =3[/tex]
Thus, the cost of a t-shirt is £3 and the cost of a hat is £2.
Learn more about linear equations at https://brainly.com/question/11897796
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Isabel's team played 8 games of basketball. During those 8 games her team's score was: 59, 65, 61, 64, 68, 57, 49 and 57. What is the median(middle)?
Answer:
60 :)
Step-by-step explanation:
The middle two numbers are 59 and 61 so you add them together and divide by 2.
On a number line , 1.38 would be located... choose all answers that make the statement true
A) to the right of 1.29
B) to the left of 1.36
C) between 0 and 1
D) between 1 and 2
Answer: A and D are the correct answers.
Step-by-step explanation:
{6.EE.B.7} Solve for x. 342 + x = 782*
Answer:
Hello There!!
Step-by-step explanation:
342 + x = 782 -342
x=440
hope this helps,have a great day!!
~Pinky~
Find the value of x. Write your answer in simplest form.
Answer:
It would be 4.
Step-by-step explanation:
Alright, this is a 30-60-90 special triangle. With special triangles, there is a formula that you can use to find unknown side lengths of a triangle if you know the angles of it.
With a 30-60-90 triangle, the sides opposite of these angles are:
30 degrees : x
60 degrees: x√3
90 degrees: 2x
With this, we can see that opposite of the 60 degrees is the length 2√3. From this, it can be found that the opposite of the 30 degrees would be 2, given the formula of the special triangle. Lastly, the unknown value would be 4, since it is two times this amount.
Answer:
x = 4
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] x = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
x = 4
calculate the area of the shaded region. someone please help!
Answer:
[tex]130cm^{2}[/tex]
Step-by-step explanation:
1) Calculate the entire rectangle and subtract the right triangle area
15 x 10 = 150 Entire rectangle area
(5 x 8) ÷ 2 = 20 Triangle area
150 - 20 = 130 Area of shaded region
If y represents a student's age, which inequality shows that you must be older than 14 to
try out for the basketball team?
A y < 14
B. y > 14
c.y > 14
D. 14 = y
Answer:
B. y > 14
y which is students age is greater than 14
What is the difference between a plane and a piece of paper?
A. Nothing, both can have lines and points on them
B. You can draw on paper not on a plane
C. You can make a piece of paper into a plane if you know how to fold it
D. A plane is two dimensional and goes on infinitely, a piece of paper has three dimensions and has definite boundaries
E. Nothing, because they are the same thing
F. Planes are used in mathematics, paper is not
Answer:
D
Step-by-step explanation:
need some funny hair jokes for math teacher plss
Answer:
Grey Hairs? Try some of our free Pi-Lights
Step-by-step explanation:
Carl and Tamera want to compare their tests in math class. They have taken six tests. Should they use the mean, median or mode to compare their scores?
Answer:
Mean
Step-by-step explanation:
I said mean because it would allow both Carl and Tamera to average their scores and compare one side by side rather than comparing 6 each which would just be time consuming and it seems like it wouldn't be any other choices.
What is the volume of a cylinder with a height of 12.8 m and a base with a radius of 5.7 m, to the nearest tenth of a cubic meter?
Answer: 1306.5 m^3
Step-by-step explanation:
1. The formula for the volume of a cylinder is: V=[tex]\pi[/tex]r^2h
2. If you substitute the values into the equation, you get
V = pi * 5.7^2 * 12.8 = 1306.5
3. 1306.5 is already to the nearest tenth, so that is the answer.
write the measure of each of the missing angle measures in the diagram above.
Answer:
<2= 65°
<3= 65°
<4= 115°
<5= 115°
<6= 65°
<7=65°
<8=115°
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Step-by-step explanation:
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Help me plss I will give u anything but pls help me
Answer:
The percentage is 1/2 * 2/5 = 1/5 = 20%.
Answer:
The correct answer is 20%
Step-by-step explanation:
If you were to pick two marbles from the pile, there would be 30 different possible combinations. Out of the 30 possible combinations, 6 of them meet the requirement of green marble on the first pick and red marble on the second pick. The fraction that represents the situation would be [tex]\frac{6}{30}[/tex] or [tex]\frac{1}{5}[/tex], which would be equal to 20%, so that is the correct answer.