10 A frustum is a portion of a solid. The frustum shown opposite is formed from a cone.
a What is the volume of the missing top cone? Give answers correct to the nearest cubic metre.
b What was the volume of the entire cone?
c What is the volume of the frustum?
Answers
Step-by-step explanation:
all you needed to do was a quick search on the internet : "volume of a cone".
and you get immediately :
pi×r²×h/3
the reason is similar to all other volume formulas : base area times height. for pyramids and cones there are factors included to reduce this a bit, because they simply don't go straight up from their base area, so they have less volume than comparable objects that do go straight up (like a cylinder compared to a cone).
r = radius
h = height
so, for a) we only need to use the calculator :
pi × 5² × 30 / 3 = pi×25×10 = 785.4 ≈ 785 m³
for b) we need to do the same thing, but with r = 10 and h = 60.
pi × 10² × 60 / 3 = pi×100×20 = 6283.2 ≈ 6283 m³
so, for c) we only need to subtract the result of a) from the result of b)
the frustum is the volume of the large cone minus the volume of small, top cone.
6283 - 785 = 5498 m³
Related Questions
1. Un terreno de cultivo en Junín tiene forma de rectángulo de 10m de base y 4m de altura. Debido a que el agricultor desea obtener mayor producción, amplía dicho terreno en dos metros cada lado. ¿En qué porcentaje aumentó el área?
Answers
Answer question worth 25 points plz help!
Answers
Answer:
B
Step-by-step explanation:
b) Convert 101, into denary number
Answers
If 101 is given in base b, then in base 10 you have
[tex]101_b = 1\times b^2 + 0\times b^1 + 1\times b^0 = b^2 + 1[/tex]
For instance, if b = 2, then
101₂ = 2² + 1 = 5₁₀
If b = 3, then
101₃ = 3² + 1 = 9₁₀
If b = 4, then
101₄ = 4² + 1 = 17₁₀
The answer depends entirely on the base of the given number.
“Angle 7 and angle 8 are complementary. Angle 5 ≅ angle 8 and the measure of angle 6 = 29. Show your work to find the measure of angle 7 and 5.”
Answers
Based on the definition of complementary angles:
Measure of angle 7 = 29°
Measure of angle 5 = 61°
What are Complementary Angles?Complementary angles have a sum that is equal to 90 degrees. If two angles are complementary, then their sum = 90 degrees.
Angle 7 and angle 8 are complementary [given]
Angle 5 and angle 6 will also be complementary
Angle 5 ≅ angle 8 [given]
Angle 7 will also be congruent to angle 6
Measure of angle 6 = 29° [given]
Measure of angle 7 = 29°
Measure of angle 5 + measure of angle 6 = 90 degrees
Substitute
Measure of angle 5 + 29° = 90°
Measure of angle 5 = 90° - 29°
Measure of angle 5 = 61°
Therefore, based on the definition of complementary angles:
Measure of angle 7 = 29°
Measure of angle 5 = 61°
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Factorize: a^3-1+ a-1
Answers
Answer:
[tex](a-1)(a^2+a+2)\\[/tex]
Hi,
Step-by-step explanation:
[tex]Remember:\ x^3-y^3=(x-y)(x^2+xy+y^2)\\a^3-1+a-1\\\\=(a-1)(a^2+a+1)+1(a-1)\\\\=(a-1)(a^2+a+2)\\[/tex]
Answer:
have a great day
god bless you
Jen has 2 quarters, 5 dimes, 3 nickels, and 2 pennies in her pocket.
Answers
2 quarters is 50 cents
5 dimes is 50 cents
3 nickels is 15 cents
2 pennies is 2 cents
50+50=1 dollar
15+2=17 ceNts
She has $1.17 in her pocket if that’s the question
Please help ASAP!!!!! Also show details
Answers
Answer:
1)
AB = 23-18.9
AB= 4.1
~~~~~~~~~~~~~~~~~
2) 5x+15 = 50
5x=35
x=7
Step-by-step explanation:
plz solve this for me as soon as possible
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]f(n)=4n-5\\\\g(n)=an+b\\\\(gof)(n)=5n+1\\\\f(g(n))=f(an+b)=4*a*n+4b-5=5n+1\\\\4an=5n ==> a=5/4\\4b-5=1 ==> 4b=6 ==> b=3/2\\\\\\\boxed{g(n)=\dfrac{5n}{4} +\dfrac{3}{2} }\\\\[/tex]
Depart London at 12:30. A 7 hour and 30 minutes videos and arrives in New York at 15:00. What is the time difference between London and New York
Answers
Answer:
Step-by-step explanation:
Well in London The time is like 12 and stops there it don't go to 13:00 like New York does so basically I'm saying London as a regular time and New York has the Military Time!
I'm not smart like 60% but help
Answers
Answer:
SEE THE IMAGE FOR SOLUTION.
HOPE IT HELPS
The slope of a line equals the “run over the rise.”
True or false
Answers
Answer:
False
Step-by-step explanation:
The slope of a line is
Change in y over change in x
This is also known as rise over run
3√20+2√125 this has to be done in the surds rules although I do not understand
Answers
3√20+2√125 = 3√(4×5) + 2√(5×5×5)
=6√5+10√5
=16√5
This is your answer .
Factorize 2x^2-5/3xy-2y^2
Answers
I hope it helps you
Answer:
[tex]y = 0 \: .x = \frac{2}{3} y[/tex]
Step-by-step explanation:
[tex] \frac{2 {x}^{2} - 5 }{3xy - 2 {y}^{2} } [/tex]
[tex]3xy - 2 {y}^{2} = 0[/tex]
[tex]y \times (3x - 2y) = 0[/tex]
[tex]y = 0 = 3x - 2y = 0[/tex]
[tex]y = 0 = 3x = 2y[/tex]
[tex]y = 0[/tex]
[tex]x = \frac{2}{3} y[/tex]
[tex]y = 0. \: x = \frac{2}{3} y[/tex]
(5a -2b +7c) + (3a + b -c) (Write answer in alphabetical order.) *
Answers
Answer:
8a - b + 6c
Step-by-step explanation:
Just combine like terms.
5a + 3a = 8a
-2b + b = -b
7c - c = 6c
calculate the gradient of the straight line which joins A(2,-3) and B(6,9)
Answers
Answer:
Gradient: m = 3
Step-by-step explanation:
m = change in y/change in x
m = [tex]\frac{Y2-Y1}{X2-X1}[/tex]
m = [tex]\frac{9-(-3)}{6-(2)}[/tex]
m = 12/4
m = 3
Reduce the Fractions 15/9to its Lowest Terms
Answers
[tex]\large\bf{\red{ \implies}} \tt \: \cancel\frac{15}{9} \\ [/tex]
[tex]\large\bf{\red{ \implies}} \tt \: \frac{5}{3} \\ [/tex]
Decimal Form - 1.6667
..A number divided by 5 is 15 how do you right it as a equation
Answers
Answer:
75
Step-by-step explanation:
Let's say the unknown number is x
x/5 = 15
x = 15*5
x = 75
What does heredity mean?
DNA make RNA, and RNA makes proteins
a human genetic disorder
traits passed down from parent and grandparents to offspring
the process of DNA replicating into two strands
Answers
Write a function C(t) to represent the cost of
renting a canoe for t hours. The rental charge
is $25 plus $2 for every 20 minutes of rental.
Find C(1.5) and describe its meaning.
Answers
Answer:
C(t)=25+2t
C(1.5)=25+2(1.5)=28
$28 for 1.5 minutes rent
A function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t and the cost for 1.5 minutes will be $28.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given that the rental charge is $25 plus $2 for every 20 minutes of rental.
The function formed for the given data will be:-
C(t)=25+2t
At 1.5 minutes the rent will be calculated as below:-
C(1.5)=25+2(1.5)=28
Therefore, the function C(t) represents the cost of renting a canoe for t hours is C(t)=25+2t, and the cost for 1.5 minutes will be $28.
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Someone please help find the answer. I already know it’s not C.
Answers
Answer:
I can't see the question
Step-by-step explanation:
Take a proper picture
You are making a smoothie that calls for 1/4 cup of yogurt. This only makes enough for 1 person and we need enough for 4 total people. How much
yogurt should you add
Answers
Answer:
2 cups of yogurt
Step-by-step explanation:
1=1/2
4=4×(1/2)
=2
The interior angle of a polygon is 108⁰ greater than the exterior angle. How many sides has the polygon
Answers
=========================================================
Explanation:
x = exterior angle
x+108 = interior angle, as its 108 degrees larger than the exterior
The two angle pairs add up to 180, since they form a straight line
exterior+interior = 180
x+(x+108) = 180
2x+108 = 180
2x = 180-108
2x = 72
x = 72/2
x = 36
The exterior angle is 36 degrees which means we have n = 360/x = 360/36 = 10 sides. This polygon is a decagon.
Answer:
10 sidesStep-by-step explanation:
Let the number of sides is n.
We know the sum of interior angles is:
180(n - 2)So each interior angle is:
180(n - 2)/nWe also know the sum of exterior angles is 360, so each exterior angle is:
360/nWe are given the difference of the interior and exterior angles:
180(n - 2)/n - 360/n = 108Solve the equation for n:
180(n - 2) - 360 = 108n180n - 360 - 360 - 108n = 072n = 720n = 10The polygon has 10 sides
6 3/4 yards of fabric per 3 costumes. how many yards do i need for 7 costumes
Answers
Finds how much is needed for 1 costume by dividing 6 3/4 by 3
6 3/4 /3 = 2 1/4 yards per costume.
Multiply yards per costume by 7:
2 1/4 x 7 = 15 3/4 yards total needed.
[tex]\\ \rm\hookrightarrow 6\dfrac{3}{4}yards=3costumes[/tex]
1costume[tex]\\ \rm\hookrightarrow \dfrac{27}{4}\div 3[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{27}{4}\times \dfrac{1}{3}[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{27}{7}yards[/tex]
7costumes[tex]\\ \rm\hookrightarrow \dfrac{27}{7}\times 7[/tex]
[tex]\\ \rm\hookrightarrow 27yards[/tex]
pls tell correct ans as fast as possible
Answers
Step-by-step explanation:
the answer is in picture
the cost price is 50
Answer:
Rs 50Step-by-step explanation:
Number of books bought = 2000Number of books sold = 2000 - 200 = 1800Cost of each book = cTotal cost = 2000cProfit = 8% of 2000cSolve for c:
2000c*0.08 = 1800(c + 10) - 2000c160c = 18000 - 200c360c = 18000c = 18000/50c = 502/7-3/8+2/5 Simplify
Answers
Answer:
0.31
Step-by-step explanation:
(2/7)-(3/8)+(2/5)
Answer:
LCM: 7,8,5 = 280
80/280 - 105/280 + 112/280
87/280
Step-by-step explanation:
Help!!! Please i need helppppoo
Answers
Hey there! I'm happy to help!
Our goal here is to write the function (equation) that represents what Carlos has graphed. This is a line, so we can use the slope-intercept equation to represent it.
Our slope-intercept equation is y=mx+b, where m is the slope and b is the y-intercept.
If we look at the graph, we see that the the line intersects the y-axis at the point (0,0), also known as the origin, so our y-intercept is 0.
To find our slope, we need to first find two points on the line. Well, we already have (0,0). The next point on the line that seems to have integers is (7,5). This means that from (0,0) our rise is 5 and our run is 7, and since slope is rise over run, that means that our slope is 5/7 (for every one unit we go over, the line goes up 5/7).
Now, we just throw these numbers into the equation.
y=5/7x
or
f(x)=5/7x (if it needs to be in that function format)
Have a wonderful day and keep on learning! :D
The box plots show the amount of time It took members of cross-country teams from two different schools to finish a two-mile run.
A. There is a weak evidence that team members from School J run slower than team members from School K.
B. There is no evidence that team members from School J run slower than team members from School K.
C. It is certain that team members from School J run slower than team members from School K.
D. There is strong evidence that team members from School J run slower than team members from School K.
Answers
Answer:
D
Step-by-step explanation:
Determine the ordered pair that satisfies the equation, 5x + 2y = 7.
A
(8. – 33 )
B
(-1,1)
C
(-4,3)
D
(5,2)
E
I don't know yet
Answers
Answer:
None of the first 4 do. so I guess the answers E.
Step-by-step explanation:
Describe the differences that exist between the informal geometric reasoning and formal thinking used to prove conjectures
Answers
Answer:
hey
Step-by-step explanation:
Formal geometric reasoning gives better information than informal geometric reasoning.
What is informal geometry?Informal Geometry is defined as the aid for understanding geometry via questioning, practices, and conjecture. Subjects include stature, balance, isometries, and proportions, with scaling as a major theme.
What is formal geometric?Formal geometry is defined as geometric explanations that are ways to formally make an opinion about a particular formation or figures in the geometrical entity, a formal geometric explanation is a detailed way to deliver that specific figures or domains which are congruent.
An an conjecture is made often using observation and detail given on the basis of logical observation is termed informal geometric reasoning,
While in formal geometric reading calculation-based approximation conjectures gives better detail of the informal geometric reasoning.
Learn more about formal geometry here:
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X^2+4x+3
--------------
x^2-1
Reduce the above expression to its lowest terms
Answers
Answer:
your answer is 4x+4
Step-by-step explanation:
x^2-1) x^2+4x+3 (1
x^2 -1
(-) (+)
4x+4
quotiend is 1
remainder is 4x+4
Answer:
your answer is 7x/-1
Step-by-step explanation:
x^2 cancels out x^2
4+3=7
therefore your answer is 7x/-1