From a circular cylinder of diameter 10 cm and height 12 cm are conical cavity of the same base radius and of the same height is hollowed out. Find the volume and the whole surface of the remaining solid.
[tex](take \ \: \pi \: = 3.14) [/tex]
Answers
Step-by-step explanation:
Now, Given that:-
Diameter (d) = 10 cm
So, Radius (r) = 10/2 = 5cm
Height of the cylinder = 12cm.
[tex]volume \: of \: the \: cylinder \: = \pi {r}^{2} h[/tex]
[tex] = > \pi \times {5}^{2} \times 12 {cm}^{3} = 300\pi {cm}^{3} [/tex]
Radius of the cone = 5 cm.
Height of the cone = 12 cm.
[tex]slant \: height \: of \: the \: cone \: = \sqrt{ {h}^{2} + \: {r}^{2} } [/tex]
[tex] = > \sqrt{ {5}^{2}+{12}^{2} } cm \: = 13cm[/tex]
Volume of the cone = 1/3 *πr^2h
[tex] = > \frac{1}{3} \pi \times {5}^{2} \times 12 {cm}^{3} = 100\pi {cm}^{3} [/tex]
therefore, the volume of the remaining solid
[tex] = 300\pi {cm}^{3} - 100\pi {cm}^{3} \\ = 200 \times 3.14 {cm}^{3} = 628 {cm}^{3} [/tex]
Curved surface of the cylinder =
[tex]2\pi \: rh \: = 2\pi \times 5 \times 12 {cm}^{2} \\ = 120\pi {cm}^{2} .[/tex]
[tex]curved \: surface \: of \: the \: cone \: = \pi \: rl \\ = \pi \times 5 \times 13 {cm}^{2} \\ = 65\pi {cm }^{2} \\ area \: of \: (upper)circular \: base \: \\ of \: cylinder \: = \\ = \pi \: {r}^{2} = \pi \times {5}^{2} [/tex]
therefore, The whole surface area of the remaining solid
= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder
[tex] = 120\pi {cm}^{2} + 65\pi {cm }^{2} + 25 \pi {cm}^{2} \\ = 210 \times 3.14 {cm}^{2} = 659.4 {cm}^{2} [/tex]
Hope it helps you!!
Related Questions
HELP WILL MARK BRAINLIEST EXTRA POINTS!!!
Answers
Answer:
Step-by-step explanation:
All of the angles will equal up to 180
10x-10=180
180+10 is 190
190=10x 190/10=x x=19 or R
<Q: 19*2=38-5=33 <Q:33
<P:133-5=128 <P:128
128+33+19=180,
Double checking to fact check the asnwers.
Which number is a solution of the inequality x less-than n3gative 4? Use the number line to help answer the question.
A number line going from n3gative 9 to positive 1.
–3
0
2
Answers
Answer:
-3
Step-by-step explanation:
because a positive minus a negative depending on what the positive = a negative
On a coordinate plane, how are the locations of the points (-7 , -4) and (7 , -4) related?A.
A. locations unrelated
B.reflection across the x-axis
C.reflection across both axes
D. reflection across the y-axis
Answers
Answer: reflection across y axis
Step-by-step explanation:
A bag has 3 balls: 1 orange (0), 1 green (G), and 1 blue (B). A coin has 2 sides:
heads (H) and tails (T).
You randomly pick a ball and toss a coin. What is the sample space?
Answers
Answer:
The sample space is
S= {BH,GH,YH,OH,BT,GT,YT,OT}
Step-by-step explanation:
The sample space refers to the set of all the possible outcomes.
The possible outcomes are:
Head and blue ball: BH
Head and green ball: GH
Head and yellow ball: YH
Head and orange ball: OH
Tail and blue ball: BT
Tail and green ball: GT
Tail and yellow ball: YT
Tail and orange ball: OT
The sample space is S= {BH,GH,YH,OH,BT,GT,YT,OT}
Kate's Cupcakes sells cupcakes in boxes of 4. Depending on the type of cupcake, a box can cost at most $20. Let x represent how much each cupcake costs. Which inequality describes the problem?
Answers
Answer:
4×<=20
×<=5
AAAAA single Cupcake can cost at most $5.
Step-by-step explanation:
A cupcake needs to be $5 each for a box of 4 to cost $20. Meaning that a cupcake (x) will be $5 or less.
Reflect the triangle in the mirror line.
Answers
The top left point will stay the same in the x-axis, and will be -4 on the y-axis
Finally, the top right point will stay true same on the x-axis, but will be -4 on the y-axis in its image.
If you could mark my answer the brainliest it would be very much appreciated!
How to solve for “?”
With work please. I know the answer just not how to get it. Thanks!
Answers
Check the picture below.
select 3 ratios that are equvilant to 5:2
Answers
Answer:
10/4
15/6
20/8
Step-by-step explanation:
Solve the following problems mentally and match it to its corresponding solution.
Pls Help
4t = 40
10 + t = 14
70 - t = 30
multiple answers , 40, 10 , 4
Answers
Answer:
1. t=102. t=43. t=40Step-by-step explanation:
Isolate the term of t from one side of the equation.
1. 4t=40First, you have to divide by 4 from both sides.
4t/4=40/4
Solve.
Divide the numbers from left to right.
40/4=10
t=102. 10+t=14First, change sides.
t+10=14
Then, subtract by 10 from both sides.
t+10-10=14-10
Solve.
Subtract the numbers from left to right.
14-10=4
t=43. 70-t=30First, subtract by 70 from both sides.
70-t-70=30-70
Solve.
30-70=-40
Rewrite the problem down.
-t=-40
Divide by -1 from both sides.
-t/-1=-40/-1
Solve.
Divide the numbers from left to right.
-40/-1=40
t=40Therefore, the correct answer is t=10, t=4, and t=40.I hope this helps! Let me know if you have any questions.
Answer:
4t =40 t= 10 4x10=40
10 + t = 14 t=4 10 + 4 = 14
70 - t =30 t= 40 70 - 40 = 30
Hope this helps!
Are the number of telephone numbers within a particular area code determined by permutations, combinations, both, or neither? Are there any restrictions? Explain your answer with details.
Answers
Answer:
Phone numbers are an example of permutations. In the United States, each phone number consists of ten digits, three for the area code and seven for the unique phone number. (There is also a "1" preceding each phone number to indicate that the first three digits are the area code.)
Step-by-step explanation:
3 no d anf
answer needed
with process
Answers
Answer:
d) ordered pairs are equal
e) ordered pairs are not equal
Step-by-step explanation:
d) ( 3+4 , 2 - 1)
x-co ordinate = 3 + 4= 7
y-co ordinate = 2 - 1 = 3
(3+ 4 , 2-1) = (7 , 3)
(3+4 , 2-1) & ( 7 ,3) are equal
f)Compare the x -co ordiante and y - co ordiante of the two pairs
p +q = q + p {addition closed under commutative property}
but q - p ≠ p - q {Subtract is not closed under commutative}
(p +q, q - p) & ( q + p , p -q ) are not equal
Which expression is equivalent to 2x^2-10x-48in factored form?
Answers
Answer: B
Step-by-step explanation:
20000 lb equals how many US tons
Answers
Answer:
10 us tons
Step-by-step explanation:
Answer:
10 Tons
Step-by-step explanation:
this is becuase 2k or 2,000 lbs is equal to 1 US Ton
simply devide the lbs by 2,000 to get the same amount in US Tons
Bob's Bagels sells 7 bagels for $8.00, and Betty's Bagels sells 9 bagels
for $6.00. Which is the better deal?
3 of 4
The better deal will have the
higher
ratio of dollars per bagel.
To find the better deal, you must compare the fractions
Select...
Comparing the fractions reveals that
Select...
has the better deal
Answers
Answer:
3 of 4
The better deal will have the higher ratio of dollars per bagel.
To find the better deal, you must compare the fractions 8/7 and 6/9.
Comparng the fractions reveals that Betty has the better deal
Step-by-step explanation:
bobbs bagels: 8/7 equals 1.14, so each bagel would cost about $1.14
bettys bagels: 6/9 equals 0.66, so each bagel would cost about $0.66
$0.66 is better than $1.14 per bagel. therefore, bettys bagels are cheaper
hope this helps :)
Please help with this geometry work asp
Answers
Answer:
x=21
y=45
z=101
Step-by-step explanation:
Angles crossing each other are congruent
86=4x+2
84=4x
x=21
Quadrilateral has 360 degrees
86 + 86 + 2y+4 + z-7 = 360
172 + 2y+4 + z-7 = 360
2y+4=94
2y=90
y=45
z-7=94
z=101
mark brainliest please!
Solve for x. The triangles in each pair are similar.
Answers
Step-by-step explanation:
similar triangles means that all angles in one triangle are exactly the same as the angles in the other triangle.
and the lengths of all sides of one triangle have the same scaling factor with the lengths of the sides of the other triangle.
so, when we compare the "features" of the triangles, we see that C corresponds to S, B to R and D to T.
so, DC (50) corresponds to TS (70).
and that means that CB (60) corresponds to SR (11x - 4).
the scaling factor from BCD to RST is 70/50 = 7/5.
that means DC × 7/5 = TS.
and CB × 7/5 = SR :
60 × 7/5 = 11x - 4
12 × 7 = 11x - 4
84 = 11x - 4
88 = 11x
x = 8
Multiplying and factoring polynomial expressions (9th grade)
Answers
Answer:
1. 2(a^2 + 3a + 9)
2. 5(x^2 - 1)
3. 3(t + 8)(t - 2)
4. n(4 - n)
Step-by-step explanation:
For 1, you can only factor out the constant from each.
For 2, you can also only factor out the constant, but remember that you include the 1 when dividing 5 by 5.
For 3, you can factor out the constant and the variables.
For 4, you can only factor out the variable.
The thickness of a book varies directly with
the number of pages in the book. A book is
1.8 cm thick and contains 350 pages. What is
the thickness of the first 84 pages of the book?
Answers
[tex]\qquad \qquad \textit{direct proportional variation}\\\\\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill }\\\\\textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill }\\\\[-0.35em]~\dotfill[/tex]
[tex]\stackrel{\textit{"th" varies directly with "p"}}{th=kp}\qquad \textit{we also know that} \begin{cases} th=1.8\\ p=350 \end{cases} \\\\\\ 1.8=k(350) \implies \cfrac{9}{5}=350k\implies \cfrac{9}{1750}=k~\hfill \boxed{th=\cfrac{9}{1750}k} \\\\\\ \textit{when p = 84, what is "th"?}\qquad th=\cfrac{9}{1750}(84)\implies th=\cfrac{54}{135}\implies th=0.432[/tex]
A City Council consists of nine men and six women. Three representatives are chosen at random to form a sub-committee. What is the probability one man and two women are chosen?
Answers
Answer:
0.2967 or 29.67%Step-by-step explanation:
Total number of people
9 + 6 = 15Combination of 3-people subcommitee without restrictions
15C3 = 15!/(15 - 3)!3! = 15!/12!3! = 15*14*13/2*3 = 455Combination of 3-people subcommitee with one man ad two women
9C1*6C2 = 9*6!/(6-2)!2! = 9*6!/4!2! = 9*6*5/2 = 135The probability of one man and two women are chosen
P = 135/455 = 0.2967 or 29.67%what ratio is equivalent to 1.5:6
Answers
Answer:
2:10:12
Step-by-step explanation:
I multiplied all of the numbers by 2
It doesn't matter what number you multiply the numbers by, as long as you multiply all 3 of them.
Simplify Each Radical Expression. Leave in radical form. (Do not use decimals.)
4. √(5) * √(5) * √(9)
Answers
[tex]\sqrt 5 \cdot \sqrt 5 \cdot \sqrt 9\\\\=\left( \sqrt 5\right)^2 \cdot \sqrt{3^2}\\\\=5\cdot 3\\\\=15[/tex]
I NEED HELP PLEASE I NEED TO KNOW HOW U GOT THE ANSWER PLEASE
Answers
Linear is basically a straight line. It can be increasing or decreasing.
Decreasing is when on the graph, when x increases, y decreases.
On the graph, there are two parts that are decreasing. Between -2 and 0, and Between 2 and 4. Let's look at these two.
- For between -2 and 0, the line is not straight. Therefore, it is decreasing and nonlinear. We can check if this is the right answer.
- For between 2 and 4, the line is decreasing. However, the line is straight, which means it is decreasing but linear.
Your final answer is B.
If 65 is 20% of x, then x = ?
Answers
Step-by-step explanation:
65/x ×100 = 20
6500/20 = x
x = 325 Answer .. option (B)
[tex] \bold{ \underline{ \purple{Question}}}[/tex]
if 65 is 20% of X then x = ?
[tex] \bold{Given}[/tex]
65 is 20% of x[tex]\bold {\underline{SOLUTION}}[/tex]
65 / 20 = x
[tex] \displaystyle\frac{65}{20} \times 100[/tex]
[tex] \displaystyle \: \frac{65}{2 \cancel0} \times 10 \cancel0[/tex]
[tex] \displaystyle \frac{65 \times 10}{2} [/tex]
[tex] \displaystyle \frac{650}{2} [/tex]
[tex]\displaystyle \frac{ \cancel {650}}{ \cancel2} [/tex]
x= 325 Answer
hence option B is correct.
if 65 is 20% of X then x = 325
What is the value of B for the following triangular prism?
Answers
It would be 48ft2. If you need help with anything just ask
need help please with info
Answers
Answer:
So the whole thing is 180, we already have 3x+12, it's C.
Because A would be 3x +180 (1803x) +something else which would bring it over 180.
Step-by-step explanation:
C is the answer because 180 is the toal and it isn't going over 180 right away.
Answer:
C. (3x +12) + x = 180°
Step-by-step explanation:
(3z+12)° is obtuse. x° is acute.
Both are supplementary angles that are linear pair that add up to 180°
(3x + 12)° + x° = 180°
4x + 12 = 180°
4x = 168°
x = 42°
Plug x into (3x + 12)°
3*42° + 12
126 + 12
138°
question is in the picture
Answers
Answer:
the avswers are
1. 100,000
2. 10,000
3. 1,000
Step-by-step explanation:
divide the number by one and then keep adding zeros
help me ive been up all night doing math
Answers
Answer:
See below ~
Step-by-step explanation:
(a)
The point (8, 28) represents that in the time of 8 minutes, 28 cm of the horse trough has been filled.
8 minutes 28 centimeters(b)
Finding the unit rate
No. of centimeters / min.28 cm / 8 min3.5 cm/minFind the volume of each prism. Please help mee and thank you.
Answers
Answer:
Step-by-step explanation:
please help me
covert 2km to m
convert 3 decimeter to mm
covert 1km to cm
Answers
Answer:
2,000 m
300 mm
100,000 cm
Step-by-step explanation:
Answer:
2 km converted to meters is 2000 meters
3 decimeters converted to millimeters is 300 mm
1 km converted to centimeters is 100,000 centimeters
Find the volume of each composite figure please help
Answers
small rectangle = 5 x 5 x 12 = 300 sq yds
Larger rectangle = 4 x 12 x 18 = 864 sq yds