Select the correct answer.
A container is made by cutting off the bottom of a cone. The container has a diameter of 30 centimeters and a height of 20 centimeters. The
small cone that was removed has a diameter of 10 centimeters and a height of 6 centimeters.
What is the volume of the container, to the nearest cubic centimeter?
A. 6,126 cm³
B. 6,283 cm³
C. 5,812 cm³
D. 5,969 cm³
Answers
The volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
Calculating VolumeFrom the question, we are to determine the volume of the container
Volume of the container = Volume of the cone - Volume of the small cone
The volume of a cone is given by the formula,
V = 1/3πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
For the small cone,
Diameter = 10 cm
∴ Radius, r = 10cm/ 2 = 5 cm
h = 6 cm
For the big cone
diameter = diameter of the container = 30 cm
∴ Radius = 30cm/ 2
Radius = 15cm
h = height of small cone + height of container
h = 6 cm + 20 cm
h = 26 cm
Putting the parameters into
Volume of the container = Volume of the cone - Volume of the small cone
We get,
Volume of the container = 1/3π × 15² ×26 - 1/3π × 5² × 6
Volume of the container = 1/3π (15² ×26 - 5² × 6)
Volume of the container = 1/3π (5850 - 150)
Volume of the container = 1/3π (5700)
Volume of the container = 1/3 × π × 5700
Volume of the container = 5969.026 cm³
Volume of the container ≈ 5969 cm³
Hence, the volume of the container is 5969 cm³. The correct option is D. 5,969 cm³
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Related Questions
Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)
Answers
Answer:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Step-by-step explanation:
Given
[tex]log_3(\frac{21}{5})[/tex]
Required
Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]
[tex]log_3(\frac{21}{5})[/tex]
Express 21 as 7 * 3
[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]
Apply law of logarithm
[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]
[tex]log_3(3) = 1[/tex]. So, we have:
[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]
Rewrite:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Sari wrote the equivalent ratios below to convert cups to fluid ounces. How many fluid oz. Are in 9 cups.
Answers
Answer:
the number of fluids ounces in 9 cups is 72 fluid ounces
Step-by-step explanation:
The computation of the number of fluids ounces in 9 cups is shown below:
As we know that
In 1 cup = 8 fluid ounces
So for 9 cup it is
= 9 × 8
= 72 fluid ounces
hence, the number of fluids ounces in 9 cups is 72 fluid ounces
I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe
Answers
Answer:
1.5 or 1 1/2 pounds of candy
Step-by-step explanation:
First, divide 2 into 4 equal pieces. You do this because of the denominator in 3/4.
2 divided by 4= 0.5
Then 0.5 times 3 because of the numerator in 3/4.
0.5 times 3= 1.5
You can convert this into the fraction 1 1/2 or you can leave it a 1.5
Hope this helps!
Solve the equation.
5x = 3x²+1
5+ 13
a
5-√13
c.
-5+ √13
5- V13
X=
or
or
12
12
6
6
b.
-5+ √13
5-√3
d.
S+~13
5- 13
Of
12
or
12
6
6
Answers
Hope this helps
In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.=
Answers
Answer: 415.2
Step-by-step explanation:
Mr. Alvarez makes a walkway of 3 cement slabs.He uses 14 cubic feet of cement to make the walkway.Each square slab has a volume of 4 cubic feet
Answers
Answer:
I suppose that you want to see how we can find the volume of each individual slab with the given information, the procedure is as follows.
The walkway has 3 cement slabs,
He uses a total amount of 14 cubic feet to make the complete walkway.
This means that the 3 cement slabs together have a total volume of 14 ft^3
To find the volume of each slab, we need to find the quotient between the total volume and the total number of slabs, then we get:
Volume of each slab = (14 ft^3)/3 = 4 ft^3
This means that each cement slab has a volume of 4 ft^3.
Answer:
6 ft^3
Step-by-step explanation:
Given the function below, what is the g(-8)?
g(x)=2x+1
Answers
Last season, Patrick Mahomes threw for 4,800 yards in 16 games. This season, he had a 15% increase in the number of yards he threw per game.
How many yards did he throw per game after the increase?
Answers
Answer:
345 yards.
Step-by-step explanation:
4800/16 = 300
300 increase 15% =
300 × (1 + 15%) = 300 × (1 + 0.15) = 345
James has 838 feet of rope. There are 17 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?
Answers
Answer:
838 ÷ 17 = 49.29 feet each
Step-by-step explanation:
divide the total rope by number of hikers equals amount of rope each hiker will receive.
I need help with a/d
Answers
Answer:
yeah whats the question asking >:(
Each letter in the word "TEXTBOOK" is written on an identical tile and placed in a bag. What is the probability of
drawing a vowel on the first try?
Answers
Answer:
37.5% or 3/8
Step-by-step explanation:
There are 8 total letters, and only 3 vowels, which can be the fraction 3/8. 3/8 as a percent is 37.5%. Hope this helps!
Answer:
Capital letters and Rotations marks
Find the value of x. Round to the nearest tenth:
Answers
Answer:
x = 13.5
Step-by-step explanation:
What is the value of 6(2b-4) when b=5?
Answers
Answer:
126
Step-by-step explanation:
Step-by-step explanation:
When b = 5 Then
6( 2b - 4)
= 6 ( 2 *5 - 4)
= 6 ( 10 - 4)
= 6 * 6
= 36
Hope it will help :)
[tex]4x\leq 12[/tex]
Answers
Divide each term by
4
and simplify.
Inequality Form:
r ≤ 3
Interval Notation:
( − ∞ , 3 ]
A pelican has a wingspan of 8 feet.
An eagle has a wingspan of 6 feet.
How much longer is the wingspan
of a pelican?
Answers
Answer:
I'm pretty sure the answer would be 2 feet.
Step-by-step explanation:
8-6=2
What is the area of the triangle?
6 square inches
18 square inches
12 square inches
30 square inches
Answers
6 square inches.
Explanation:
You should use 4 for the base and 3. If you used the formula to find the area of the triangle, then you should get 6 for your answer.
Answer:
answer is 6.
Step-by-step explanation:
the base as 4 in. times the height as 3in. divided by 2= 6in.
Enumere Cuatro Fuentes de Corriente continua
Answers
Answer:
La corriente continua es producida por fuentes como baterías, termopares, celdas solares y máquinas eléctricas de tipo conmutador de tipo dínamo. La corriente continua puede fluir en un conductor como un cable, pero también puede fluir a través de semiconductores, aislantes o incluso a través de un vacío como en los haces de electrones o iones. espero que esto te ayude
The diagram shows two right-angled triangles. PQR and QST are straight lines. It is given that sin x = [tex]\frac{15}{17}[/tex] . Find the value of cos y.
Answers
Step-by-step explanation:
[tex] \sin(x) = \frac{15}{17} = \frac{23 + c}{34} \\ 34 \times 15 = 17(23 + c) \\ 510 = 391 + 17c \\ 17c = 119 \\ c = 7[/tex]
[tex] \sin (y) = \frac{7}{25} \\ y = 16.26 \\ \cos(16.26) = \frac{ \alpha }{25} \\ 0.96 = \frac{ \alpha }{25} \\ \alpha = 24 [/tex]
[tex] \cos(y) = \frac{24}{25} [/tex]
help please
4 − ( −12) + ( −7) =
Answers
............................................9
someone solve please
Answers
What statement describes the expression 10 +1/4× (5+3)-3
Answers
Answer:
The answer would be 9.
Step-by-step explanation:
10 + 1/4 x (5 + 3) - 3
10 + 1/4 x (8) - 3
10 + 2 - 3
12 - 3
9
Given the following parallelogram: Solve for x.
7x + 70
16x - 20
Answers
Answer:
x=10
Step-by-step explanation:
7x+70=16x-20
70=9x-20
9x=90
x=10
You have a friendship club. There are 12 members in your club. On the twelfth day of each month, you have a friendship call. Each member of the club talks to every other member that day by phone. This way everybody expresses his or her friendship with each other. How many conversations are made on that day?
Answers
Answer: There are a total of 66 conversations.
Step-by-step explanation:
Ok, we have 12 members.
let's call them:
member 1, member 2, member 3, etc...
Let's assume that member 1 starts talking to the others, then he talks to:
member 2, member 3, member 4, etc.
So member 1 talks to the other 11 members.
We have already 11 conversations.
Now let's count the conversations of member 2.
He talks to member 1, member 3, etc.
But the conversation between member 1 and member 2 was already counted, so we do not count it this time, then here we have other 10 conversations.
now for member 3. He talks with member 1, member 2, member 4, member 5, etc...
But conversations between member 1 and member 3, and member 2 and member 3 are already counted, so here we have 9 new conversations.
We already can see the pattern here.
For each new member that we count, the number of conversations is one less than for the previous member.
The total number of conversations will be:
11 + 10 + 9 + 8+ 7 + 6+5 + 4 + 3+ 2+ 1 = 66
A rectangular lettuce patch, 560 square feet in area, is to be fenced off against rabbits. Find the least amount of fencing required if one side of the land is already protected by a barn. What are the dimensions?
Answers
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 560 square feet, hence:
Area = length * width
560 = xy
y = 560/x
One side of the land is already protected by a barn, hence:
Perimeter (P) = x + x + y = 2x + y
P = 2x + y
P = 2x + 560/x
For least amount of fencing, dP/dx = 0, hence:
dP/dx = 2 - 560/x²
0 = 2 - 560/x²
560/x² = 2
2x² = 560
x = 16.7
y = 560/16.7 = 33.5 ft
The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft
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The slope is 2.92, which shows a positive relationship because it is a positive number. The
longer a person’s hair, the more it will cost to get the hair highlighted. This makes sense, as
more product is required to highlight more hair.
Answers
These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
4 m
6 m
8 m
9 m
6 m
Answers
Answer:
4m i think it sounds about right
Answer: the answer is 9m or D
Step-by-step explanation:
17.
Is the relation a function? Why or why not?
{(–8, –4), (–2, 0), (1, 3), (–2, 6)}
A. Yes; only one range value exists for each domain value.
B. No; the relation passes the vertical line test.
C. No; two range values exist for domain value –2.
D. Yes; two range values exist for domain value –2.
Answers
Answer:
C. No; two range values exist for domain value –2.
Step-by-step explanation:
The relation is not a function.
The -2 in the domain repeats
Since
x
=
−
2
produces
y
=
0
and
y
=
6
, the relation
(
−
8
,
−
4
)
,
(
−
2
,
0
)
,
(
1
,
3
)
,
(
−
2
,
6
)
is not a function.
The relation is not a function.
Which of the following are properties of the circumcenter of a triangle? Check
all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Answers
Answer: A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
C. The circumcenter is equidistant fromeach vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Step-by-step explanation:
The properties of the circumcenter of a triangle from the options given include:
• The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
• The circumcenter is equidistant fromeach vertex of the triangle.
• The circumcenter is equidistant from each side of the triangle.
Option B is wrong as the circumcenter of an obtuse triangle is not always outside it. For the circumcenter, there is intersection of all the three lines and it's not important that they should always be outside.
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answers
Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
The width A rectangle is 3 cm less then its length. The perimeter of the rectangle is 30 CM. Find The length and width of the rectangle
Answers
w = l - 3
w = 9 - 3
w = 6
//
l = 9
w = 6
//
p = 2(9) + 2(6)
p = 30