What is the volume of the geometric solid produced by the triangle below
when it is rotated 360 degrees about the vertical axis YZ? *
Answers
Answer:
The volume of the geometric solid produced is 391 cubic cm ⇒ A
Step-by-step explanation:
When a right triangle is rotated about its vertical leg 360°, then it formed a cone its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle.
The rule of the volume of the cone is V = [tex]\frac{1}{3}[/tex] π r² h, where
r is the radius of its baseh is the length of its height∵ Triangle XYZ is rotated 360° about the vertical side YZ
∴ It formed a cone with a radius = XZ and a height = YZ
∵ [tex]\frac{YZ}{XZ}=tan(60)[/tex]
∵ YX = 6√3
∴ [tex]\frac{6\sqrt{3}}{XZ}=tan(60)[/tex]
∵ tan(60) = √3
∴ [tex]\frac{6\sqrt{3}}{XZ}[/tex] = √3
→ By using cross multiplication
∴ 6√3 = XZ(√3)
→ Divide both sides by √3
∴ 6 = XZ
∵ XZ = r and YZ = h
∴ r = 6 and h = 6√3
→ By using the rule of the cone above
∵ V = [tex]\frac{1}{3}[/tex] (π) (6)² (6√3)
∴ V ≅ 391 cm³
∴ The volume of the geometric solid produced is 391 cubic cm
Related Questions
CAN SOMEONE HELP ME ! Please and thank you.
A car dealership likes to have 4 blue cars on the lot for every 3 white cars. At this rate, how many white cars will be on the lot when there are 16 blue cars?
Answers
Answer:
12 white cars
Step-by-step explanation:
Our ratio is 4:3
16:?
We can determine white cars by dividing 16/4 to find how many more cars we have than our original ratio.
16/4 = 4
3 x 4 = 12
16:12 = 4:3
Answer:
Step-by-step explanation:
15
Mrs. Barnes gave her class 30 minutes of
recess after lunch. Rachel and Diamond
spent 4 minutes on the monkey bars, 7
minutes jumping rope, and 5 minutes
playing tag. How much longer do they
have for recess?
Answers
Answer:
14
because 4plus 7 plus5 equealas 16 and 30 minuse 16 equals 14
A recipe requires 7/8 stick of butter for each 1 1/4 cups of flour. Find the unit rate of sticks of butter to cups of flour.
Answers
Let R = unit rate
R = (7/8) ÷ 1_1/4
R = (7/8) ÷ (5/4)
R = (7/8) • (4/5)
R = (7/2) • (1/5)
R = 7/10
Jania makes $30,000 per year. Income tax is 32% of her total income. How much does she pay in taxes?
Answers
Answer:
9,600
Step-by-step explanation:
You take 32% of 30,000 and boom
Ex plane how knowing 50 x 4 = 200 helps you find 500 x 400
Answers
example 500 x 400 = 200000 because 5 x 4 is 20 and 500 and 400 have 2 zeros each so u add 4 zeros to 20 so 200000
can u help me thank you
Answers
Answer:
I believe the answer choice you already selected is correct.
Answer:
The slope is 2.
Step-by-step explanation:
(0,-5),(20,35)
m=y²-y¹/x²-x¹
m=35-(-5)/20-0
m=40/20
m=2
X-2
——=5
3
I am supposed to solve for x but I have no clue how
Answers
Answer:
4
Step-by-step explanation:
Answer:
x = 17
Step-by-step explanation:
Nice set up. It's very clear.
Multiply both sides by 3
3(x-2)
===== = 5 *3
3
Cancel the 3 on the left. Combine the right.
x - 2 = 15
Add 2
x - 2 + 2 = 15 + 2
x = 17
==============
(17 - 2) / 3
15/3
5
The right hand side is also 5
I need to Write an explanation of how find the slope of a line given points A (1,5) B (-7,8) can someone help me please!
Answers
Answer:
finding slope
Step-by-step explanation:
So slope is the change in y over the change in x, to show (Y/X). So finding the difference or the change usually means you need to subtract which you do to the x and y values. So you subtract the y's and x's and what you get is the change.
Idk wby it sets it up so weird in word form so imma just put this here
Answers
Answer:
141/2, 279/4
Step-by-step explanation:
Answer: wow ur right like ummm
Step-by-step explanation: wby lol
Evaluate the expression x + 3y - 4(z - 3) when x = 4, y = 6 and z = 5
Answers
4 + 3(6) - 4(5 - 3)
First solve what is inside the parenthesis.
4 + 3(6) - 4(2)
Then simplify.
4 + 18 - 8
Use PEMDAS.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
4 + 18 = 22
22 - 8 = 14
The answer is 14.
Hope I helped:)
7) A different stock loses half of its value every 2 months. If the original price was $128,
how much is it worth after 14 months.
Answers
Hello!!!!! Could someone please explain to me in a simple manner what the slope intercept form is as well as what the point slope form is? Are they the same thing? What does form mean? Thank you soooo much in advance!!!
Answers
Answer:
Step-by-step explanation:
They're both ways of expressing the equation of a line. Depending on the information you're given, it's easier to use one or the other. Like if you're given the slope and y intercept, it might be easier to use slope intercept equation. If you're given 2 points on a line, it might be easier to calculate the slope between them and then use the pointslope equation using one of the two points given to find the euqation of the line. Let me know if there's more I need to clarify
write an inequality to represent the product of x and 7 is at least 15
Answers
Answer:
[tex]7x\geq 15[/tex]
Step-by-step explanation:
This problem lays out pretty clearly what needs to be done.
First, we know that we are writing an inequality.
Then, it tells us that we need 'the product of x and 7'. A product is the result of multiplication, so we can multiply 7 and x together to get 7x.
Next, it tells us that the product (7x) is at least 15. At least means that the product has to greater than or equal to 15. That clue tells us which inequality symbol will be used.
Put it all together and:
[tex]7x\geq 15[/tex]
Hope this helped!
quick question
what if i want my own room but there are six kids and only two rooms then what do i do
ps: its not a math question
Answers
Answer:
ask your parents
Step-by-step explanation:
Step-by-step explanation:
i honestly don't know I can't help with that
Shalah mowed 12 lawns in 3 hours. What is her RATE? *
help me plz
Answers
Answer: I think the answer is 4 because usually when you find the rate of something it means you divided the two numbers or however many numbers you have... So, 12 divided by 3 is 4... So, 4 hours for each lawn she mows... or something like that... So, 4 lawns per hour...
Final answer is 4 lawns per hour... If this isn't the correct answer i am very sorry... Stay safe and have a great weekend!!! :D
Answer:
4 lawns per hour
Step-by-step explanation:
4 lawns per hour or 1 lawn per 15 mins.
12/3 is the unit rate so 4/1.
Hope this helps plz hit the crown :D
f(t) = t² – 2t; Find f(-7)
Answers
Answer:
f(-7) = 63
General Formulas and Concepts:
Order of Operations: BPEMDAS
Substituting and EvaluatingStep-by-step explanation:
Step 1: Define
f(t) = t² - 2t
f(-7) is t = -7
Step 2: Solve
Substitute: f(-7) = (-7)² - 2(-7)Exponents: f(-7) = 49 - 2(-7)Multiply: f(-7) = 49 + 14Add: f(-7) = 63Which expression is equivalent to 350−−√⋅22−−√?
1522−−√
1511−−√
3022−−√
3011−−√
Answers
Answer:
it looks like d to me
Step-by-step explanation:
Answer:
The answer is D. [tex]30\sqrt{11}[/tex]
good luck!
The top of a 16-ounce can of a drink is three times thicker than the sides and bottom (so that the flip-top opener will work properly), and the can has a volume of 473 cubic centimeters. What should the radius and height of the can be in order to use the least possible amount of metal? [Assume that the entire can is made from a single sheet of metal, with three layers being used for the top.]
Answers
A nutritionist wants to study the effects of storage time
(6, 12, & 18 months) on the amount of vitamin C present
in freeze dried fruit. Vitamin C is measured in milligrams
per 100 milligrams of fruit. Six fruit packs were randomly
assigned to each of the three storage times.
The treatment is ?
Answers
The values are missing in the question. They are : 16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2
Step-by-step explanation:16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2
We calculate sample mean and std deviation from given data.
Sample Mean, =269.8/10=26.98
Sample Variance, =1859.496/9=206.610667
Sample std dev,s==√206.610667≈14.373958
We want to test two tailed hypothesis:
: σ=12
: σ≠12
Given: s=14.373958⇒ =206.610667,n=10
Significance level, a=0.1 Degrees of freedom, df=n-1=9
Since this is two tailed test, we need area of α=0.1 on either side of critical value. This means area of 0.05 on right of positive critical value.
Critical values are given by with 9 degrees of freedom.
We can use chi-square table or following excel commands:
CHISQ. INV(0.95,9)=3.32511284307
CHISQ. INV (0.05,9)=16.9189776046
Critical Values, =3.325 and =16.919
Since this is two tailed test, the decision rule or rejection criteria is:
Reject null hypothesis if test statistic is less than or equal to left critical value OR more than or equal to right critical value, i.e,
Reject if ≤3.325 OR ≥16.919
Test statistic is given by =((9)*206.610667)/144=12.913167
Test statistic, =12.913
since test statistic is between two critical values, we (do not reject ) (i.e, we fail to reject .
Conclusion: There is (not sufficient) evidence to conclude that standard deviation is not equal to 12 .
Alternatively, we can use p-value approach. The decision rule or rejection criteria is: reject null hypothesis if p-value is less than or equal to significance level (α), i.e, reject if p-value ≤0.1
P-value is twice the (smaller) tail area of test statistic because this is two tailed test. We can use excel function to find this. 2*M IN (CHISQ.DIST (12.913167,9, TRUE ) 1-CHISQ.DIST 12.913167,9, TRUE ) =0.333149809868
P-value =0.3331
since p-value is greater than significance level (α),we (do not reject ) (i.e, we fail to reject ).
Conclusion: There is (not sufficient) evidence to conclude that standard deviation is different from 12 .
IM IN A TIMED TEST 30 MIN LEFT
Which is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
Answers
Answer:
d
Step-by-step explanation:
Answer:
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
Step-by-step explanation:
First, solve for two points which solve the equation and plot these points:
First Point: For
x=0
0−2y=6
−2y=6 then divide it by -2
y=(0.-3)
second point:
x−(2⋅0)=6
x−0=6
x=(6,0)
What is the constant of proportionality?
Answers
Answer:
To find the constant of proportionality we use the formula k= y/x so we have k=20/500 =0.04
Step-by-step explanation:
1. Doug digs a hole that is 1.7 feet below ground
level. He plants a bush that is 3 2/10 feet tall from
the bottom of the root to the top branch. How
much of the bush is above the ground?
Answers
Answer:
1.5 feet of the Bush is still above ground
Step-by-step explanation:
3 2/10= 3.2
3.2-1.7=1.5
How did the temp. change if at first it increased by 25% and then decreased by 40%?
Answers
Answer:
The temperature would have dropped 15 degrees so it would have been colder
Step-by-step explanation:
A student factors a^6 - 64 to (a^2-4)(a^4 + 4a^2+ 16).
Which statement about (a^2 - 4)(a^4 + 4a^2 + 16) is correct?
Answers
Answer:
Option (b) is correct.
The expression is equivalent, but the term is not completely factored.
Step-by-step explanation:
edge 2020
Can somebody help me with this math question plz
Answers
Step-by-step explanation:
hope this helps, happy learning!!!
Similar Triangles, find value of X
Answers
Y + 196355
I NEED TO VENT PLEASEEEEE HELP
Answers
y+196355 equals y+196355 or 196355y
but most likey it just stays the same
Answer:
196355y
Step-by-step explanation:
you can vent to me
im so counfused right now please help
For the equation 6 - m = 3, how many solutions are there for m?
0
1
infinite
2
Answers
Answer:
1.
Step-by-step explanation:
The only way to get 3 as an answer to (6-m) is if m were to equal 3. Think about how many numbers can you replace m with to make the statement true. For example, try putting 1 as your m and see if it works. 6-1=3 -> 5=3. as you can see, this statement isnt true. The only solution that would work to make this statement true is one number, 3. Hope this helps.
Negative one plus negative four
Answers
Answer:
-5
Step-by-step explanation:
-4+(-1) A negative number added by another negative number will stay negative.( like a positive number by a positive will be positive.)
Kayla works in a shoe store and is paid a 12% commission on her sales. In January, her sales total was $3,740. About how much did Kayla earn in commission for January?
Answers
Answer:
Kayla had $3,740 x .12 = 448.80 by January.
Step-by-step explanation: