A frustum is made by removing a small cone from a similar large cone. Work out the volume of the frustum, below. Give your answer in terms of pie
Answers
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h
=1/3π(R²H-r²h)
=1/3π(4.5²×9-3²×6)
=1/3π×9×3(4.5×1.5-2)
=9π(6.75-2)
=9π×4.75
=42.75π cm³
The volume of frustum of cone is \(42.75\pi\)
What is frustum of cone?Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base.
Volume of frustum of cone = \(\frac{\pi H}{3} [ R^{2} + r^{2} + rR]\)
Where,
R = Radius of the bigger circular end
r = radius of the smaller circular end
H = height of frustum
According to the question
Original height of cone = 9 cm
Radius of the bigger circular end = 4.5 cm
Radius of the smaller circular end = 3 cm
Height of frustum = 3 cm
Volume of frustum of cone = \(\frac{\pi H}{3} [ R^{2} + r^{2} + rR]\)
= \(\frac{\pi 3}{3} [ 4.5^{2} + 3^{2} + 4.5*3]\)
= \(\pi [ 20.25 + 9 + 13.5]\)
= \(42.75\pi\)
Hence, The volume of frustum of cone is \(42.75\pi\) .
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Related Questions
Earn points, answer both questions!
Answers
Answer:
Area of five squares = 1289.09 square units
Perimeter = 194.6 units
Step-by-step explanation:
Area of square and perimeter:
First find the length of each square, then find the area of each square.
To find the area of five squares, add all the area of each square.
Side of square1 = 27 units
\(\sf Side \ of \ square2 = \dfrac{2}{3}*27=2*9 = 18 \ units\\\\Side \ of\ square3= \dfrac{2}{3}*18=2*6=12 \ units\\\\Side \ of \ square4=\dfrac{2}{3}*12=2*4=8 \ units\\\\Side \ of \ square5=\dfrac{2}{3}*8=\dfrac{16}{3}=5.3 \ units\)
Area of square1 = 27*27 = 729 square units
Area of square2 = 18*18 = 324 square units
Area of square3 = 12*12 = 144 square units
Area of square4 = 8*8 = 64 square units
Area of square5 = 5.3*5.3 = 28.09 square units
Area of five squares = 729 + 324 + 144 + 64 +28.09
= 1289.09 square units
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Perimeter of the composite figure = (27 + 27+27+9) + (18+18+6) +(12+12+4) + (8+8+2.7)+ (5.3+5.3+5.3)
= 90 + 42 + 28 + 18.7 + 15.9
= 194.6 units
the perimeter is 194.6 units
Jack read 20 pages of a book in 60 minutes. How many pages can he read in 75 minutes at the same rate? Write a proportional equation. Please help me answer this equation!!
Answers
Answer:
25 pages
Step-by-step explanation:
Create a proportion:
\(\frac{pages}{minutes}\) = \(\frac{20}{60}\) = \(\frac{x}{75}\)
Cross multiply and solve for x, the number of pages in 75 minutes:
60x = 1500
x = 25
So, he can read 25 pages in 75 minutes at the same rate
He read 1 page in 3 minutes for 60 minutes 75 is 15 more than 60 so what time 3 would equal 15 It would be 5 so you would add 5 more pages to the 20 pages and you would get 25
The radius of a sphere is 6 units.
Which expression represents the volume of the sphere, in
cubic units?
27(6)
031(0)3
O 2A(12)2
lo (12)
Answers
Answer: 4/3 π 6³
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a sphere: 4/3 π r³
Replacing with the values given:
V = 4/3 π 6³
If we solve the expression:
V = 4.18 (6)^3
V = 904.77 cubic units
Feel free to ask for more if needed or if you did not understand something.
an adult blue whale can eat about 40 million Krill a day write this number in a scientific notation
Answers
how are the mertic units kilometer and kilogram the same? How are they different
Answers
Step-by-step explanation:
This units are used in measuring.
Kilometre=to measure the length
kilogram=to measure the mass
similarities differences
they measure 1000 times a value one is for mass, one is for length
well that's it really
hope this helps
Which pair of points forms a vertical line segment that is 4 units long? A. (–3, 5) and (–7, 5) B. (3, –8) and (3, –4) C. (2, 1) and (2, 3) D. (2, 4) and (–2, 4)
Answers
Answer: (-7,5) and (-3,5) :) there for answer is A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Pls help! Will give brainliest!!
Answers
Considering area (A) of garden as 30 square feet:
30 = x(2x+7)
Now we need to expand it:
x(2x+7) = 2x^2 + 7x
2x^2 + 7x = 30
Adding this into an Algebra calculator gives us 5/2 or 2.5
So x = 2.5
To prove this:
2(2.5) + 7 = 12
14 * 2.5 = 30
(2x+7) x = 30
you can distribute to make this easier
2x^2 + 7x = 30
you can plug this into quadratic formula by setting the equation =0, so:
2x^2 +7x -30 = 0
where 2x^2 = a
7x = b
and -30 = c
you can plug this into your calculator and get an answer of
X = 2.5
please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!
Answers
The function for the points are y = -15x - 5
How to determine the functionFrom the information given, we have that;
The points are;
(1/3,0) (-2 3/4,0) and (0,-5)
Using the point-slope form of a linear equation, we have;
y - y₁ = m(x - x₁)
Such that;
m is the slope of the liney - y₁ and (x - x₁) are the pointsUsing (1/3, 0) and (0, -5), we have that the slope is;
m = (0 - (-5))/0 -1/3)
expand the bracket
= 5 / (-1/3)
= -15
Now, take any of the given points and substitute the values
Using (1/3, 0), we get;
y - 0 = -15(x - 1/3).
y = -15x - 5.
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The function for the points solved by (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)
We have given the points:
(1/3,0) (-2 3/4,0) and (0,-5)
Using the formula of linear equation
\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)
Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)
that is 1/3 = \(a\), 0 = \(a_{1}\) and
0 = \(b\), -5 = \(b_{1}\)
\(x\) refers to the slope of line (take any variable)
Now for finding the value of \(x\),
\(x=a-a_{1}/b-b_{1}\)
inserting the values,
\(x=[0-[-5]]/[0-1/3]\\x= -15\)
Substitute the value of \(x\) in the equation
\(a-0=-15[b-1/3]\)
By simplifying the equation, we get
\(a=-15b-5\)
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A rectangle measures 2 1/4 meters by 1 7/8 meters. What is its area??
Answers
Hello!
2^1/4 * 1^7/8
= 0.5 * 0.125
= 0.0625
Step by step equation:
Separate the whole numbers and fractions.
Whole numbers: 2, 1
Fractions: 7/8, 1/4
Now simplify the fractions.
To make the fractions have even denominators we must multiply 1/4 by 2 on the top and bottom, changing 1/4 into 2/8.
Now that the fractions are simplified we multiply them together. 7/8 • 2/8 = 14/8. We now turn this into a mixed number, 1 and 6/8’s.
Now let’s multiply the whole numbers,
2•1 = 2. Now that we have all the numbers laid out let’s combine them.
2 + 1 + 6/8 = 3 6/8’s. Since this is out area you want to make sure to label the product correctly and the label here is meters so the answer would come out to be:
3 6/8’s meters sq.
Hope this helps!
(8x+1/2)+(4x-5 1/2) please help me
Answers
Answer: 6x-25 will be your answer
Step-by-step explanation:
80% of the 55 coffee mugs at Kari's Pancake House are dirty. How many dirty coffee mugs are there at the pancake house?
Answers
Answer:
44
Step-by-step explanation:
80% of 55=44
The diameter of a circle is 8 kilometers. What is the angle measure of an arc bounding a
sector with area 6pi square kilometers?
WILL MARK BRAINLIEST PLEASE HELP ME PLEASE
Answers
Answer:
270°
Step-by-step explanation:
Full circle length is 2πr= πd= 8π
6π/8π= x/360
3/4= x/360
x= 3*360/4
x= 270°
The center is a typical value.
It is the _______________ value of a dot plot.
Answers
When referring to a dot plot, scatter graph, or scatter plot such as this one, the line that represents the averages of all Y values is known as a line of best fit.
Hope this helps,
Jeron
:)
Answer:
When referring to a dot plot, scatter graph, or scatter plot such as this one, the line that represents the averages of all Y values is known as a line of best fit.
Step-by-step explanation:
question : ill mark brainlist
3. The ______ projection shows the size and shape of continents accurately but distorts water areas.
A. Conic
B. Mercator
C. Robinson
D. Interrupted
Answers
The correct answer is A. Conic projection.
A conic projection is a type of map projection created by projecting the surface of a globe onto a cone. The cone is then unrolled and flattened to create a two-dimensional map. Conic projections are best for mapping small areas, such as individual countries or states. They are also good for mapping areas that are located near the equator.
Conic projections show the size and shape of continents accurately, but they distort water areas. This is because the cone is tangent to the globe at one point, and the further away from that point you get, the more distortion there is.
Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.
Robinson projection is a map projection presented by American cartographer Arthur H. Robinson in 1963. It is a compromise projection that attempts to balance the distortions of area, shape, and distance. The Robinson projection is neither conformal nor equal-area, but it is pseudocylindrical, which means that the meridians are straight lines and the parallels are circles.
Interrupted projection is a type of map projection that is interrupted at regular intervals. This is done to reduce the distortion of the map. The most common type of interrupted projection is the Mercator projection, which is interrupted at the equator and the prime meridian
Given that the function graphed is ƒ(x), what is ƒ(−5)?
I will give the best answer brainliest!
Answers
Answer:
D. 5
Step-by-step explanation:
yeah-ya............. right?
The scale of the architectural drawing is 2 inches = 5 feet. If a building is 10 inches wide on the drawing, how wide will it be in real life?
A
35 feet
B
20 feet
C
30 feet
D
25 feet
Answers
Answer:
The answer is D!
Step-by-step explanation:
Firs you have to do 10 divided into 2, the answer is 5. Now you have to do 5 x 5 that will get you 25. So D is the answer! (25 feet)
If you have any question ask me please! :)
im failing math rn and really need help so pls help. Find the value of xin the triangle shown below.
Answers
Answer:
x = 10
Step-by-step explanation:
Pythagorean Theorem = a² + b² = c²
6² + 8² = c²
36 + 64 = c²
100 = c²
c = 10
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
10
Step-by-step explanation:
pythagorean thereom
6^2 + 8^2 = c^2
100 = C^2
c = 10
ANSWER QUICK PLS
look at the trapezium below, work out the size of angle
angle tuv
angle vwt
give your answer in degrees
Answers
Answer:
Step-by-step explanation:
107 is the answerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
HELP ASAP PLEASE WILL GIVE BRAINLIEST
Bryce measured the elementary school and made a scale drawing. The scale he used was 6 millimeters = 2 meters. What is the scale factor of the drawing?
Answers
Answer:
It was probally a wall because of the length of the drawing
Step-by-step explanation:
PLEASE HELP ME ASAP I DONT WANT TO FAIL
Answers
I hope this helps
Answer:
y = 3 and x = -4
Step-by-step explanation:
hope u dont fail :)
Please I don't have much time Help me please!!!
Answers
Answer:
C
Step-by-step explanation:
The shape moves to the left by 8 and up by 7.
Answer:
C
Step-by-step explanation:
on the x axis the shape moves 8 to the right and on the y it moves 7 up
Lin needs to save up $20 for a new game. How much money does she have if she has saved 75% of her goal?
Answers
Answer: She has $15
Step-by-step explanation:
20*0.75=15
Kenji is playing the video game Dragon Tamer, where players go on adventures finding and training dragons. In the first level of the game, he gets 10 points for finding a Silverthorn Dragon but gets –6 points when it scorches him with fire. What is Kenji's score at the end of the first level?
Answers
Help, I need someone to find x in this!
Answers
And since it is a right angled triangle the unknown angle is 90
So
8x + 4x + 6 + 90 = 180
12x + 96 = 180
12x = 180 - 96
12x = 84
Divide both side by coefficient of x which is 12
x = 7
Check:
8(7) + 4(7) + 6 + 90 = 180
56 + 28 + 6 + 90 = 180
180 = 180
So therefore x is 7
I would like some help
Answers
There are 5 cities listed. The mean is 273, so the total calls should be 5 x 273 = 1,365.
Find the total of know calls: 244 + 353 + 235 + 311 = 1143.
The calls in Thornbury are: 1365 - 1143 = 222
Answer:
I cant view the image??
Step-by-step explanation:
please answer all 3 questions iĺl give brainliest if right tysm
Answers
Answer:
1. 500
2. 126
3. 615
Step-by-step explanation:
Area of a parallelogram formula: A = bh
20 x 25 = 500
7 x 18 = 126
20.5 x 30 = 615
2. 7 x 18 = 126 in2
3. 30 x 20.5 = 615 yd2
Hope this helps
Indicate the sign relationship and how to solve it. -28+13
Same signs
Different signs
add
subtract
Answers
sure tho
Answer:
15 different signs
Step-by-step explanation:
Could you please help me!!
Answers
Answer:
A. 21.2 m
Step-by-step explanation:
The perimeter of a polygon is the sum of its side lengths. A square is a polygon with four sides, all the same length. You can add up the side lengths, or you can take advantage of multiplication to do the repeated addition.
P = 4s
P = 4(5.3 m) = 21.2 m
The distance Yani walked was 21.2 meters.
Answer:
21.2 Meters
Step-by-step explanation:
The perimeter is 4n where n is the length of one side of a square.
1 side of the square patio is 5.3 meters.
4(5.3)=21.2
Consider the inequality x>7. Determine whether each value of x shown in the table makes this inequality true. Select Yes or No for each value.
WILL GIVE BRANLIEST
Answers
Answer:
No no yes yes no
Step-by-step explanation:
-22>7
this is not true because -22 is less than 7 and the inequality is going toward it.
-7>7
this is also not true because of the same reason.
13>7
This is true becuase 13 is greater than 7. If you can't tell which number is greater. Subtract the first number from the second; if it is positive, it is greater. If it is 0 then it is equal. If it is negative then it is less than.
5>7
same as before
-39>7
same as -22
Aso, the values are the substitute for x.
2. no -7
3. yes 13>7
4. no 5<7
5. no -39<7
The base of the pyramid below is a square that has an area of 64 square inches.
Suppose that the pyramid is sliced so that the cross-section is a square with an area of 49 square inches.
How can you slice the pyramid to get that square?
Answers
Answer:
If you sliced the pyramid parallel to the base, the cross-section would be shaped like a square
Answer:
Slice it parallel to the base
Step-by-step explanation: