Answers
Given:
Radius of the cone = 6
Slant height of the cone = 10
To find:
The lateral area, surface area and volume of the cone.
Solution:
Let h be the height of the cone. By Pythagoras theorem, we get
[tex]10^2=(6)^2+h^2[/tex]
[tex]100=36+h^2[/tex]
[tex]100-36=h^2[/tex]
[tex]64=h^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{64}=h[/tex]
[tex]8=h[/tex]
The lateral area of a cone is:
[tex]A_L=\pi rl[/tex]
[tex]A_L=\pi (6)(8)[/tex]
[tex]A_L=48\pi[/tex]
The surface area of a cone is:
[tex]A_S=\pi rl+\pi r^2[/tex]
[tex]A_S=\pi (6)(8)+\pi (6)^2[/tex]
[tex]A_S=48\pi +36\pi[/tex]
[tex]A_S=84\pi[/tex]
Volume of cone is:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
[tex]V=\dfrac{1}{3}\pi (6)^2(8)[/tex]
[tex]V=\dfrac{288}{3}\pi [/tex]
[tex]V=96\pi [/tex]
Therefore, the lateral area of a cone is [tex]48\pi[/tex] sq. units, the surface area of a cone is [tex]84\pi[/tex] sq. units and the volume of the cone is [tex]96\pi[/tex] cubic units.
Related Questions
4n -6 = 10n
Simplify.
Answers
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Answer: n = -1
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add 6 to both sides of the equation.
4n − 6 = 10n
4n − 6 + 6 = 10n + 6
-----------------------------------------------------------------------------------------------------------------
simplify.
(add the numbers)
4n − 6 + 6 = 10n + 6
4n = 10n + 6
4n = 10n + 6
-----------------------------------------------------------------------------------------------------------------
subtract 10n from both sides.
4n − 10n = 10n + 6 − 10n
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simplify. (again)
(combine like terms) (combine like terms)
4n − 10n = 10n + 6 − 10n −6n = 10n + 6 − 10n
−6n = 6
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divide both sides by the same term.
−6n/−6 = 6/-6
n = 6/−6n = 6/−6
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simplify. (again)
(cancel terms that are in both the numerator and denominator)
n = 6/−6
(divide the numbers)
n = 6/−6
n = 1
-----------------------------------------------------------------------------------------------------------------
Answer:
n= -1
Step-by-step explanation:
You are constructing a concrete landing pad for a helicopter. You have 4704 cubic feet of concrete
If the landing pad is a square that is 56 feet on each side, how thick will the pad be
The pad will be feet thick
If you want to use the concrete to build a circular landing pad with the same thickness as the square landing pad, what would the diameter of that landing pad be?
The diameter will be feet
(Use 3.14 for pi Round the answer to the nearest hundredth)
Answers
Answer:
Round it to the nearest hundredth
Step-by-step explanation:
The perimeter of the figure below is 219.1 cm. Find the length of the missing side.
14.6 cm
15-5 cm
15-5 cm
15.5 cm
15.5 cm
15-5 cm
15-5 cm
15-5 cm
15-5 cm
32 cm
32 cm
?
Answers
Answer:
16.5
Step-by-step explanation:
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answers
Answer: the correct answer should be 160 but you said that didnt work so try 480
Step-by-step explanation:
I just did base times Hight 8*10 which is 80*6=480
hoped this helps:))
Answer:
80
Step-by-step explanation:
V= Bh/3
Area of base= (L × W) ÷2
(8×6)÷2 = 24
Multiply by height
24×10=240
Divide by 3 (since its a pyramid therefore has 3 sides)
240/3=80
80 is your answer
Please help ! Please help!
Answers
Bailey makes a conjecture that the product of two odd integers is always an odd integer. Which choice is the best proof of her conjecture
Answers
Answer:
D.
Step-by-step explanation:
Let (2a+1) be an odd number, and let (2b+1) be another odd number. The product 2(2ab+a+b)+1 is a multiple of 2 plus 1, which is an odd number.
find the HCF of 12;28 and 32
Answers
Answer:
4
Step-by-step explanation:
28 = 22 • 7
12 = 22 • 3
32 = 25
Which model is 85% shaded?
Done
Answers
Answer:
I would need to see the models to answer this question.
Answer:
?
Step-by-step explanation:
Geometry Question!!!
Answers
9514 1404 393
Answer:
12.5 cm
Step-by-step explanation:
Triangle IDA is a 3-4-5 right triangle with a scale factor of 5. That is, segment AI is 25 cm long. Since IS is half the length of the diagonal, it is ...
IS = (25 cm)/2
IS = 12.5 cm
__
If you like, you can work out the length of AI using the Pythagorean theorem:
AI² = DI² +DA²
AI = √(15² +20²) = √(225 +400) = √625 = 25
A box contains 3 black pens, 7 blue pens and 5 red pens. Without replacing the first pen,
what is the probability of pulling a red or blue pen?
Answers
Answer:12/15
Step-by-step explanation: first you add 7+5=12
then add 12+3=15
Can you help me thanks!
Answers
Which of the following shows the extraneous solution to the logarithmic equation log7 (3x ^ 3 + 7) - 100 + (x) = 27
Answers
Answer: X=-4
Step-by-step explanation:
Should be B on Edge.
Answer: X = -4
Step-by-step explanation:
I NEED HELP PLEASE ASAP!
Answers
Answer:
Step-by-step explanation:
Can someoneee please help me
Answers
9514 1404 393
Answer:
37°
Step-by-step explanation:
The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.
∠1 = 37°
__
Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.
The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.
is X greater than less than or equal to 106 degrees
Answers
Answer:
Less
Step-by-step explanation:
Please help I don’t understand it
I need a reason for both
Answers
9514 1404 393
Answer:
23) insufficient number of corresponding sides/angles
24) insufficient number of corresponding sides/angles
Step-by-step explanation:
In general, you need at least 3 corresponding parts to show triangle congruence. At least one of those must be a side. The attachment shows the ways triangles can be declared congruent. (HL works for right triangles, because we know the right angles are congruent to each other.)
__
23) A side is shown congruent (KL ≅ GH), and we know the vertical angles at J are congruent. However, we need another angle before we can declare the ∆GHJ congruent to anything. (One more side doesn't do it, because the two sides would not be on either side of the angle at J.)
Reason: insufficient data
__
24) A side is shown congruent (MP ≅ QS), and an angle is shown congruent (∠M ≅ ∠Q). As in the previous problem, we need at least one more angle, or we need to know that MN ≅ QR before we can declare the triangles congruent.
Reason: insufficient data
Factor the expression completely.
35 + 2x2 – 24
Answers
Answer:
[tex]2x^{2} +11[/tex] cannot be simplified further
Step-by-step explanation:
Determine whether
25m/
5
is equivalent to each of the following expressions.
Equivalent
Not equivalent
25m-1
252m-1
52m-1
Answers
Answer:
(a) and (b) are not equivalent
(c) is equivalent
Step-by-step explanation:
Given
[tex]\frac{25^m}{5}[/tex]
Required
Determine an equivalent or nonequivalent expression
[tex](a)\ 25^{m-1[/tex]
We have:
[tex]25^{m-1[/tex]
Apply law of indices
[tex]25^{m-1} = \frac{25^m}{25}[/tex]
This is not equivalent to [tex]\frac{25^m}{5}[/tex]
[tex](b)\ 25^{2m - 1}[/tex]
We have:
[tex]25^{2m - 1}[/tex]
Apply law of indices
[tex]25^{2m - 1} = \frac{25^{2m}}{25}[/tex]
This is not equivalent to [tex]\frac{25^m}{5}[/tex]
[tex](c)\ 5^{2m-1}[/tex]
We have:
[tex]5^{2m-1}[/tex]
Apply law of indices
[tex]5^{2m-1} = \frac{5^{2m}}{5^1}[/tex]
[tex]5^{2m-1} = \frac{5^{2m}}{5}[/tex]
Evaluate the numerator
[tex]5^{2m-1} = \frac{25m}{5}[/tex]
This is an equivalent expression
twenty subtract from 28
Answers
Answer:
8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
20-28= -8
Answer Choices
A. -0.01
B. 2
C. 0.01
D. 10,000
Answers
Answer:I hink its B if its not im sorry
Step-by-step explanation:
Jose reads his book at an average rate of 2.5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read 20 pages?
Answers
it would take him 32 minutes. You could use divisoin and multiplecation to figure it out
Carl paid $40 for 12.5 gallons of gas.After calculating,he said that the cost per gallon was about 31 cents per gallon.Is there anything wrong with Carl's thinking?.
Answers
Answer:
Well yes, because it should have cost $3.2 PER gallon
Step-by-step explanation:
Divide 40 by 12.5 to find out how much of a per gallon costs! Hope it helps.
A rectangular prism is 4 cm long, 3 cm wide and 8 cm tall. What is the volume of the prism?
Answers
Answer:
96 cm³
Step-by-step explanation:
v = 4 x 3 x 8 = 96 cm³
Answer:
The volume of the prism is 96cm^3
Step-by-step explanation:
You multpily 4*3*8=96
Tina walked her dog 12 blocks. This is twice the number of blocks she walked yesterday. How far did Tina walk her dog yesterday?
Answers
Answer: Hello, your Answer is Below ^^
Your Answer Is 6
Step-by-step explanation:
I Got the answer 6 Because 6 x 2 = 12
Tina Walked 12 blocks and Half of 12 Is 6
Hope this helps you!
Have a great Day!
~Rainbow~
Answer:
the correct answer is 6
Step-by-step explanation:
since twice = 2 you'll need to do 12 divided by 2
which is equal to 6.
or you can simply just think what number is twice in 12.
Li’s family is saving money for their summer vacation. Their vacation savings account currently has a balance of $2,764. The family would like to have at least $5,000.
The inequality 2764 + x Greater-than-or-equal-to 5000 can be used to determine the amount of money the family still needs to save. What is the solution to the inequality?
x Greater-than-or-equal-to 2236
x Greater-than-or-equal-to 7764
x Less-than-or-equal-to 2236
x Less-than-or-equal-to 7764?
Answers
Answer: x greater-than or equal-to 2,236
Step-by-step explanation:
5,000-2,764= 2,236
so Li's family still needs to save at least $2,236
Answer:
A
Step-by-step explanation:
bc
hi can you please help me with my work
Answers
Answer:
3 expodent 12
Step-by-step explanation:
Jamal's car averages 18.4 miles per gallon. How far can he expect to drive on 9.2 gallons of gas?
Answers
Answer:
169.28
Step-by-step explanation:
18.4x9.2=169.28
Solve for the following by
FACTORING:
x2 + 15x + 56 = 0
Answers
Answer:
17x + 56 = 0
Step-by-step explanation:
add 2x and 15x
Question 7Partially correct answer. Your answer is partially correct. Try again.An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.(a) Is there evidence that the success rate is greater for longer tears
Answers
This question is incomplete, the complete question is;
An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.
a) Is there evidence that the success rate is greater for longer tears? Use alpha=0.05
Answer:
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
Step-by-step explanation:
Given the data in the question;
Sample of tears greater than 25;
number of successive repairs X₁ = 13
number of repair n₁ = 19
proportion of successive repairs [tex]p[/tex]₁ = 13/19 = 0.68
q₁ = 1 - [tex]p[/tex]₁ = 1 - 0.68 = 0.32
Sample of tears shorter than 25;
number of successive repairs X₂ = 22
number of repair n₂ = 30
proportion of successive repairs [tex]p[/tex]₂ = 22/30 = 0.73
q₂ = 1 - [tex]p[/tex]₂ = 1 - 0.73 = 0.27
so;
H₀ : There is no significant difference in the successive proportions; [tex]p[/tex]₁ = [tex]p[/tex]₂
Hₐ : The successive rate is greater for longer tears [tex]p[/tex]₁ >
Significance level ∝ = 0.05
Test Statistics
Z = ([tex]p[/tex]₁ -
so we substitute
Z = ( 0.68 - 0.73 / √[ (0.68 ×0.32 / 19) + ( 0.73×0.27 / 30 ) ]
Z = -0.05 / √[ 0.01802 ]
Z = -0.05 / 0.1342
Z = -0.37
P-value for the given test, p = P( Z > -0.37 )
= 1 - P( Z ≤ - 0.37 )
= 1 - 0.35569
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
9.3+b=−42 , you would subtract 9.3 to isolate the variable.
Answers
Answer:
yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b