A cone has radius 9 and a height 12. A frustum of this cone has height 4.
What are the radii of the bases of the frustum?
What is the slant height of the frustum?
What is the lateral area of the frustum?
(If you waste an answer it will be removed so don't try and get "Free" points.)
Answers
Answer:
Part A)
The lower base has a radius of 9 units, and the upper base has a radius of 6 units.
Part B)
5 units.
Part C)
75π or about 235.62 square units.
Step-by-step explanation:
Please refer to the figure below.
The cone has a radius of 9 units and a total height of 12 units.
A frustum of the cone has a height of 4 units.
Part A)
The lower radius of the frustum will simply be 9 units.
For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:
[tex]\displaystyle \frac{12}{8}=\frac{9}{x}[/tex]
Solve for x. Simplify:
[tex]\displaystyle \frac{3}{2}=\frac{9}{x}[/tex]
Cross-multiply:
[tex]18=3x\Rightarrow x=6[/tex]
The upper base has a radius of 6 units.
Part B)
We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:
[tex]SH^2=12^2+9^2[/tex]
Simplify:
[tex]SH^2=225\Rightarrow SH=15\text{ units}[/tex]
Now, find the slant height of the upper cone:
[tex](SH_\text{cone})^2=8^2+6^2=100[/tex]
So:
[tex]SH_\text{cone}=10[/tex]
Then the slant height of the frustum will be the cone subtracted from the total. Thus:
[tex]SH_{\text{frustum}}=15-10=5\text{ units}[/tex]
Part C)
We can first find the lateral area of the entire cone. The lateral area is given by:
[tex]LA=\pi r\ell[/tex]
The lateral area of the entire cone will be:
[tex]LA=\pi (9)(15)=135\pi[/tex]
The lateral area of the upper cone will be:
[tex]LA_\text{cone}=\pi(6)(10)=60\pi[/tex]
Then the lateral area of the frustum is:
[tex]LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2[/tex]
Related Questions
8
Which expression is equivalent to 4.8 + 2.2w – 1.4w + 2.4?
Answers
Answer:
7.2 + 0.8w
Step-by-step explanation:
Combine like terms.
Here Like terms: i) 2.2w and (-1.4w)
II) 4.8 and 2.4
4.8 + 2.2w - 1.4w + 2.4 = 4.8 + 2.4 + 2.2w - 1.4w
= 7.2 + 0.8w
The commuting distances, in miles, of 10 employees were used to make the box plot shown above. Which of the sets of distances below matches the given box plot?
A.
Commuting Distances: 10, 15, 15, 20, 20, 30, 30, 30, 45, 45
B.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 45, 45, 45
C.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 30, 45, 45
D.
Commuting Distances: 10, 15, 20, 20, 20, 20, 30, 30, 45, 45
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
How many proportional relationships are shown in the coordinate plane below?
Choose 1 answer:
a. 0
B. 1
c.2
d.3
Answers
Answer:
0
Step-by-step explanation: i did the lesson
A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 6800 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xxx, the number of 100-kilogram crates that can be loaded into the shipping container.
Answers
Answer:
x ≤ 207 crates
Step-by-step explanation:
Greatest weight of the container = 27,500 kilograms
Weight of other shipment = 6,800 kilograms
Weight of a crate = 100 kilograms
Number of 100-kilogram crates that can be loaded into the shipping container = x
The inequality is
27,500 ≤ 6800 + 100x
27,500 - 6800 ≤ 100x
20,700 ≤ 100x
x ≤ 20,700 / 100
x ≤ 207 crates
Arc AD=98 and I need help with both problems below
Answers
Answer:
arc DC = 64
angle DCQ = 32
Step-by-step explanation:
Hello There!
The circumference of a normal circle is 360
Given that arc AD = 98 and having found arc ABC we can find arc DC by subtract the known arcs from 360
360 - 98 - 198 = 64
Hence arc DC = 64
The problem wants us to find angle DCQ having found arc DC
Remember like stated before an included angle is equal to 1/2 its opposite arc
64/2=32
so angle DCQ = 32
Consuelo recorded the amount of time, in minutes, she spent exercising on the treadmill. 15, 25, 30, 25, 45, 20, 35, 30, 35, 30, 40 Which value best represents the mode? 10 min 10 min 30 min 30 min 35 min 35 min 25 min
Answers
Answer: 30 mins.
Step-by-step explanation:
The mode is the value that appears the most times.
In such a situation, first order the numbers in an ascending order:
15, 20, 25, 25, 30, 30, 30, 35, 35, 40, 45
As can be seen from the above, 30 is the number that appears the most so the mode is 30 mins.
a charm on a lucy's bracelet had the dimensions shown what is the area of the charm
Answers
Answer:
13
Step-by-step explanation:
please help me this is for a grade
Answers
Answer:
b
Step-by-step explanation:
Can someone help me on this it’s been giving me a hard time
Answers
Given:
QRST is an isosceles trapezoid with RS||QT.
To find:
The value of x, angle R and angle T.
Solution:
If a transversal line intersect two parallel lines then the sum of same sides interior angles is 180 degrees.
[tex]m\angle Q+m\angle R=180[/tex]
[tex](6x-22)+(8x+34)=180[/tex]
[tex]14x+12=180[/tex]
[tex]14x=180-12[/tex]
[tex]14x=168[/tex]
Divide both sides by 14.
[tex]x=\dfrac{168}{14}[/tex]
[tex]x=12[/tex]
Now,
[tex]m\angle R=(8x+34)^\circ[/tex]
[tex]m\angle R=(8(12)+34)^\circ[/tex]
[tex]m\angle R=(96+34)^\circ[/tex]
[tex]m\angle R=130^\circ[/tex]
We know that the base angles of an isosceles triangle are equal.
[tex]m\angle T=m\angle Q=(6x-22)^\circ[/tex]
[tex]m\angle T=(6(12)-22)^\circ[/tex]
[tex]m\angle T=(72-22)^\circ[/tex]
[tex]m\angle T=50^\circ[/tex]
Therefore, [tex]x=12,\ m\angle R=130^\circ[/tex] and [tex]m\angle T=50^\circ[/tex].
During an local election the ratio of teens to adults who voted was 9.3. If 732 people voted how many were teens
Answers
Answer: 549
Step-by-step explanation:
Given
The ratio of teens to adults is 9:3
The total number of people who voted is 732
let 9x be the no of teens and 3x be the no of adults such that their ratio is 9:3
So, we can write
[tex]\Rightarrow 9x+3x=732\\\Rightarrow 12x=732\\\Rightarrow x=61[/tex]
No of the teens were [tex]9x=9\times 61=549[/tex]
how many square metre of carpeting are needed to cover a floor that measures 8m by 5m
Answers
Answer:
40 meters squared
Step-by-step explanation:
8 * 5 = 40
y = 7x + 19
-21 x 3y = 57
Answers
Answer:
x= -2 y= -5
Step-by-step explanation:
If You Had Three Wishes, What Would You Wish For?
Answers
Answer:
I would wish to be the brainliest, I would wish for more points, and i would wish for more people to answer my questions
Step-by-step explanation:
thats only for brainly though
Answer:
My three wishes would be:
1: Get all staright A's
2: the sickness that starts with C thats going around goes away forever
3: Have some cheesecake.
Step-by-step explanation:
The measure of one interior angle of a parallelogram is 5 times the measure
of another angle. What's the measurement of the larger interior angle?
Answers
Answer:
Step-by-step explanation:
The sum of these adjacent angles must sum to 180 degrees (also the sum of all angles must be 360)
a+5a=180
6a=180
a=30
The larger angle is 5a so the larger angle is
5(30)=150 degrees.
Find the circumference of the circle with the given area A. Use 3.14 for TI
A = 87.9
C =
r=
Answers
87.9/3.14 = around 28
Square root of 28 = 5.3
The radius is 5.3
Circumference: diameter * 3.14
5.3 + 5.3 = 10.6
10.6 * 3.14 = 33.3
The circumference is 33.3
Find the interest
earned:
$26,000 for 36 months
at 7.5% annual
compound interest
Answers
Answer:
Interest = $6,300 (Approx.)
Step-by-step explanation:
Given:
Amount deposit (P) = $26,000
Number of month = 36 month
Number of year (n) = 36 / 12 = 3 year
Rate of interest (r) = 7.5% = 0.075
Find:
Interest earned
Computation:
Interest = p[(1+r)ⁿ-1]
Interest = 26,000[(1+0.075)³-1]
Interest = 26,000[(1.075)³-1]
Interest = 6,299.71
Interest = $6,300 (Approx.)
Which is a simplified form of the expression -9(y + 1) + 5y?
Answers
Answer:
Your answer is -4y - 9
Step-by-step explanation:
Simplify the expression.
~Brainiliest please~
help me please thanks
Answers
Answer:
two
Step-by-step explanation:
i used a calculator
At the beginning of March, a store bought a rake at a cost of 9$ and marked it up 130%. At the end of the month, the rake had not sold, so the store marked it down 50%. What is the discounted price?
Answers
Answer:
the new discounted price is $5.85
Step-by-step explanation:
First convert 130% into a decimal: 130 ÷ 100 = 1.3
Next multiply 1.3 by 9: 9 x 1.3 = 11.7
Then convert 50% into a decimal: 50 ÷ 100 = 0.5
Last multiply 11.7 by 0.5: 11.7 x 0.5 = 5.85
2
Help what is the product of 46x10
Answers
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
less than 100 students want to start at 9:00 am true or false
for there are 17
Answers
1.
A. 4.4%
B. 104.1%
C. 4.2%
D. 0.042%
Answers
Answer:
D. 0.042%
Step-by-step explanation:
YOUR ANSWER
Graphical form: T%2Ahef%2Aor%2Amu%2Alar=A%5EP-1g%2Aiv%2Aest%2Ahei%2Ant%2Aer%2Aes%2Atr%2Aat%2Aer simplifies to T%2Ahef%2Aor%2Amu%2Alar-A%5EP%2Bg%2Aiv%2Aest%2Ahei%2Ant%2Aer%5E2%2Aes%2Atr%2Aat=0
Text form: T*hef*or*mu*lar=A^P-1g*iv*est*hei*nt*er*es*tr*at*er simplifies to T*hef*or*mu*lar-A^P+g*iv*est*hei*nt*er^2*es*tr*at=0
Cartoon (animation) form:
For tutors: simplify_cartoon( T*hef*or*mu*lar=A^P-1g*iv*est*hei*nt*er*es*tr*at*er )
If you have a website, here's a link to this solution.
DETAILED EXPLANATION
Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes T%2Ahef%2Aor%2Amu%2Alar=A%5EP-g%2Aiv%2Aest%2Ahei%2Ant%2Aer%2Aes%2Atr%2Aat%2Aer.
Look at .
Reduce similar several occurrences of highlight_red%28+er+%29 to highlight_green%28+er%5E2+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-A%5EP+%29,highlight_green%28+g%2Aiv%2Aest%2Ahei%2Ant%2Aer%5E2%2Aes%2Atr%2Aat+%29
It becomes .
Result: T%2Ahef%2Aor%2Amu%2Alar-A%5EP%2Bg%2Aiv%2Aest%2Ahei%2Ant%2Aer%5E2%2Aes%2Atr%2Aat=0
A
Question 14
Jabar earns $5 for the first 10 pounds of newspaper he recycles, then 50 25 for each additional pound. Which expression ropresents the amount he earns for recycling p pounds of newspaper if p > 10?
5+0.25 (p-10)
(5 +0.25) P
5 +0.25p
5 (10) +0.25p
B
С
D
Answers
Complete Question
Question 14
Jabar earns $5 for the first 10 pounds of newspaper he recycles, then $0.25 for each additional pound. Which expression represents the amount he earns for recycling p pounds of newspaper if p > 10?
a. 5+0.25 (p-10)
b. (5 +0.25) P
c. 5 +0.25p
d.5 (10) +0.25p
Answer:
5 (10) +0.25p
Step-by-step explanation:
Let the number of additional pounds = x
Hence:
Jabar earns $5 for the first 10 pounds of newspaper he recycles, then $0.25 for each additional pound.
The statement above is represented as:
$5 × 10 + $0.25 ×p
= 5(10) + 0.25(p)
Therefore, the expression that represents the amount he earns for recycling p pounds of newspaper if p > 10 is written as
5(10) + 0.25(p)
Option d is the correct option
What is the value of x?
Answers
Answer:
x = 39
Step-by-step explanation:
The angle between a tangent and the radius of a circle at the point of contact is 90° , then
x = 180 - (90 + 51) = 180 - 141 ← angle sum of triangle
x = 180 - 141 = 39
x + 51 = 90
x = 90 - 51
x = 39°
how many times can 10 go into 111?
Answers
Answer:
11 times
Step-by-step explanation:
hope this helps
Answer:
11.
Step-by-step explanation:
10 x 10 = 100
10 x 11 = 110
10 x 12 = 120 which is too much so its the one above.
You are putting money into a bank account. You start with $100 and add $12 every month. The total amount of money in your account can be represented by the following equation. (where T is total amount and M is the number of months):
T = 100 + 12 M
If you have $208, how many months have passed?
Show the equation and how you got the answer.
Answers
100
Add 12 every month
Ex: 100 + 12
100 + 12 + 12+ 12+ 12+ 12+ 12+ 12+ 12+ 12
It wound not be 100 x 9 because 100 x 9 is 900
Therefore 9 months
9 x 12 = 108
so that would be 100+108= 208
Hope this helps~
Bonnie's doctor recommended that she drink 2cups of milk per day. If she buys 3 quarts of milk,will it be enough milk to last 1 week?
Answers
Answer:
She does not have enough milk to last for 1 week
Step-by-step explanation:
From the question, we are told that:
Bonnie's doctor recommended that she drink 2cups of milk per day.
Step 1
The number of days in a week is 7 days
Hence
1 day = 2 cups of milk
7 days = x
Cross Multiply
x = 7 × 2 cups of milk
= 14 cups of milk.
Step 2
If she buys 3 quarts of milk,will it be enough milk to last 1 week?
We have the conversion rate as:
1 quart = 4 cups
Therefore,
1 quart = 4 cups
3 quarts = x cups
Cross Multiply
x cups = 3 quarts × 4 cups/1 quart
x cups = 12 cups of milk
This means she bought 12 cups of milk.
Therefore, from the above calculation, she does not have enough milk to last for 1 week because due to her doctor's recommendation, she need 14 cups of milk for the week but she only bought 12 cups of milk
Answer:
70
Step-by-step explanation:
68+2
Select the graph that correctly represents the
armount of money. y. Jack earns doing
chores for x hours at $2 an hour if he works
for a maximum of 8 hours.
Answers
Answer: C
Step-by-step explanation: Because 2 times 1= 2 2times 2=4 2 times 3=6 etc...
What are the measurements of angle 1 and angle 2
Answers
Angle 2 is 120 degrees
Sallie is earning $8.70 per hour and got a 6% increase in her pay. What is sallies new rate of pay?
Answers
8.70*(6/100)=0.522 that's the increase
then we add it to the base salary
8.70+0.522=9.222$