Given:
Sum of the radius of the base and height of a cylinder = 21 cm
Curved surface area of the cylinder = 616 sq.cm
To find:
The total surface area of the cylinder.
Solution:
Let r be the radius of the base and h be the height of the cylinder.
Sum of the radius of the base and height of a cylinder = 21 cm
[tex]r+h=21[/tex]
[tex]h=21-r[/tex] ...(i)
Curved surface area of the cylinder is
[tex]CSA=2\pi rh[/tex]
Curved surface area of the cylinder = 616 sq.cm
[tex]2\pi rh=616[/tex]
[tex]2(\dfrac{22}{7})r(21-r)=616[/tex]
[tex]44r(21-r)=616\times 7[/tex]
[tex]21r-r^2=\dfrac{616\times 7}{44}[/tex]
[tex]21r-r^2=14\times 7[/tex]
[tex]0=98-21r+r^2[/tex]
[tex]0=98-14r-7r+r^2[/tex]
[tex]0=14(7-r)-r(7-r)[/tex]
[tex]0=(7-r)(14-r)[/tex]
[tex]r=7,14[/tex]
Using (i), for r=7, h=14 and for r=14, h=7.
Total surface area of the cylinder is
[tex]A=2\pi r(r+h)[/tex]
For r=7 and h=14,
[tex]A=2(\dfrac{22}{7})(7)(7+14)[/tex]
[tex]A=44(21)[/tex]
[tex]A=924[/tex]
For r=14 and h=7,
[tex]A=2(\dfrac{22}{7})(14)(14+7)[/tex]
[tex]A=88(21)[/tex]
[tex]A=1848[/tex]
Therefore, the total surface area of the cylinder is either 924 sq.cm or 1848 sq. cm.
plz answer the question step by step
Answer: x = 59°, y = 114°.
Step-by-step explanation:
The sum of the opposite angles of a quadrilateral in a circle is 180°.
y = 180° - 121° = 59°
The two angles being adjacent makes a total angle of 180° on the straight line.
x = 180° - (180°-114°) = 180° - 66° = 114°
What is the value of x?
Enter your answer in the box.
x =
Answer:
Step-by-step explanation:
The two triangles are similar and therefore we can set up a proportion
9/(9 + 72) = (3x - 20)/(3x - 20 + 56) Combine like terms on the right
9/(81) = (3x - 20)/(3x + 36) Cross multiply
9(3x + 36) = 81 (3x - 20) Remove the brackets.
27x + 324 +1620 = 243x Add 1620 to both sides
27x + 324 + 1620 = 243x Subtract 27x from both
1944 = 216x divide both sides by 216
x = 9
If you feel comfortable canceling the size of the numbers can be reduced.
9/81 = 1/9
1/9 = (3x - 20)/(3x + 36)
3x + 36 = 9(3x - 20)
3x + 36 = 27x - 180
36 + 180 = 24x
216 = 24x
216/24 = x
x = 9
There is another cancelation possible, but this is simple enough.
Is the following equation true or false? Explain your reasoning.
(x + 8)2 = x2 + 64
Answer:
False
Step-by-step explanation:
An angle measures 24º more than the measure of its complementary angle. What is the
measure of each angle?
What are the two angles please hurry
Answer:
33, 57
(not 100% sure this is correct)
Step-by-step explanation:
90= x +(24 +x)
(drag 90, plus the x's and drag the 24)
90 = 2x + 24
(Subtract 24 from 24 and 90 from 24)
66 = 2x
(Divide both by two)
33 = x
(now use x and plus it by 24)
24 + x = 57
Maria correctly answered 16 of the 20 questions. What fraction of the questions did she answer correctly?
To solve 5/7 - 2/n = 1/21
Answer:
Step-by-step explanation:
Lol u think AM smArt to hice You the answer
Elsie bought a video game for 85$. if the store charges 170% of its cost for the game, how much is the store's profit?
Answer: $59.5
170/100 * 85 = 144.5
144.5 - 85 = 59.5
If that is wrong my next guess is $144.50
The time required to empty a tank varies as inversely as the rate of pumping. If a pump can empty a tank in 45 min at the rate of 600 kl/min, how long will it take the pump to empty the same tank at the rate of 1000 kl/min?
okk
Step-by-step explanation:
hii
am
Jack
from
United State
America
Answer:
27 minutes.
Step-by-step explanation:
R = k/t
Substituting given info
600 = k/45
k = 45 * 600 = 27000
So the relation is S = 27000/t
So if R = 1000
1000 = 27000/t
t = 27000/ 1000
t = 27.
can someone help me with this?
Answer:
12
Step-by-step explanation:
51 ÷ 3 = 17
204 ÷ 17 = 12
hope this helps
A: The perimeter of a rectangular garden is 376 m. If the length of the garden is 99 m, what is its width?
B: The area of a rectangular window is 7007 cm If the width of the window is 77 cm, what is his length?
Answer:
A) the width is 89
B) if area is 7007, the length is 91
Step-by-step explanation:
Answer:
A: 89 m
B: 91 m
Step-by-step explanation:
A: P=2(L+W)
P=2L+2W
P=2(99)+2W
2W=376-198=178
W=178/2=89m
B: A=L×W
7007=L×77
L=7007/77=91
L=9l m
What expression is equivalent to
15n + 20r
Answer: 5(3n+4r)
Step-by-step explanation:You need to find the gcf/factor .So the gcf of 15 and 20 is 5.So know that you know the gcf ,you divide 15n by 5 which gives you 3n and divide 20r by5 which gives you 4r.Now the last thing you do is,take the GCF which is 5 and place a Parentheses and take 3n and 4r and add them together.
So you get 5(3n+4r) as your expression that is equivalent to 15n + 20r .
Hope it helps . :)
Find the surface area of the rectangular prism using its net
Answer:
62
Step-by-step explanation:
3 x 5 = 15
3 x 2 = 6
2 x 5 = 10
15 x 2 = 30
6 x 2 = 12
10 x 2 = 20
30 + 12 + 20 = 62
A figure in the first quadrant is translated down and to the right. Is it known what quadrant the image is in?
what is the equation in point-slope form of the line passing through (2,5) and (-1,8)?
Answer:
y=-1x+7
Step-by-step explanation:
A graph showing a proportional relationship will...
PLS PLS HELP!!!! Write and solve an inequality to find the possible values or x if the area of the
rectangle is < 56 feet squared.
2 ft
(3x + 4) ft
Answer:
width=2 ft, length=(3x+4)ft
Area of Rectangle=width x length
=2ft . (3x+4)ft
=6x+8 ft sq
Area of Rectangle <56 ft sq
6x+8 ft sq <56 ft sq
6x < 56 ft sq - 8 ft sq
6x < 48 ft sq Substeracting 8 on both sides
6x/6 < 48 ft sq/6 Dividing by 6 on both sides
x < 8 ft sq
Step-by-step explanation:
What is the volume of a frustum of a right pyramid with the area of the lower base square to 100 square inches, the area of the upper base equal to 25 square inche,and the altitude equal to 12 inches
Answer:
1
Step-by-step explanation:
The points (-2, 6) and (3, __ ) are data values of an inverse variation. Fill in the missing value.
Answer: y=6
Step-by-step explanation:
It is inverse so you know it’s y=k/x. Taking the first orders pair you find that k= -12. Then if you put it in y= -12/-2 you get 6 therefore y=6. Your welcome
I’ll pay you if you help me
Answer: help you with what?
Step-by-step explanation:.-.
Haha. No need of money. But ask the question..
waiting..
would y=x be proportional or nonproportional?
A student estimated that it would take 3 hours to write a book report, but it actually took her 5 hours. What is the percent error for her estimate?
Answer:
Overage of actual vs. predicted: 2 hours
Step-by-step explanation:
Her Error is 100(2/3) = 66.7%
I NEED HELP PLEASE ASAP
Answer:
Answer choice C is correct
Step-by-step explanation:
Use the line of best fit to determine the y-value when the x-value is 7.
A. 25
B. 37
C.53
D.42
Answer:
53
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
(R/s)(3) = ? Please hurry
What is the volume of this aquarium
Answer:
You can also divide the number of cubic inches by 231 to get the volume in gallons. For example, let's calculate the volume of a rectangular tank that is 20″ long, 12″ wide, and 10″ high.
Step-by-step explanation:
Cuatro amigos están en un equipo de baloncesto. Durante un juego, cada amigo llevaba un registro de cuántos tiros intentaron y cuántos de esos intentos hicieron. ¿Qué amigo tuvo el mejor récord en cuanto al número de disparos realizados?
Henry acerto 0.45 de sus tiros
Allison hizo 4/15 de sus tiros
Arthur acerto 8/20 de sus tiros
Trevor fallo el 58% de sus tiros
Answer:
Allison tuvo el mejor récord
Step-by-step explanation:
If there are 4 apples for every 5 oranges, and there are 16 apples, how many fruits are there altogether?
Answer:
36
Step-by-step explanation:
4:5
16:n
16÷4=4
4×5=20
16:20
16+20=36
Answer:
36 fruits (I'm not sure, but I think it's correct)
Step-by-step explanation:
4 apples = 5 oranges
16 apples = ? oranges
4 x ? = 16
4 x 4 = 16
5 x 4 = 20
4 apples = 5 oranges
16 apples = 20 oranges
16 + 20 = 36 fruits
Vector B has x, y, and z components of 3, 7.2,
and 4.5 units, respectively.
Calculate the magnitude of B
Answer:
[tex]\approx 9.0\:\mathrm{units}[/tex]
Step-by-step explanation:
The magnitude of 3D vector [tex]\vec{v}[/tex] can be given by the following:
[tex]| \overline{v}| =\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}[/tex]
Plugging in given values, we have:
[tex]| \overline{v}|=\sqrt{3^2+7.2^2+4.5^2},\\| \overline{v}| \approx \fbox{$9.0\:\mathrm{units}$}[/tex].
Find the vertex angle of the figure below B = 40 egrees
Step-by-step explanation:
it's an Equilateral triangle
the base angels are equal
A=100°
B=40°
C=40°
The required vertex angle will be 100° in the given figure.
What is an Isosceles Triangle?An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.
The triangle given in the figure is an Isosceles triangle.
It is given that side AB is equal to side AC.
So ∠B = ∠C = 40°
Now we know that the sum of angles of a triangle is equal to 180°. So here in this triangle ABC. These are the sum of these three angles will be equal to 180.
As per the given figure,
∠A + ∠B +∠C = 180°
∵ ∠B = ∠C = 40°
∠A + 40° +40° = 180°
∠A + 80° = 180°
∠A = 180° - 80°
∠A = 100°
Therefore, the required vertex angle will be 100° in the given figure.
Learn more about Isosceles Triangle here:
brainly.com/question/2456591
#SPJ5
If w is 15 when z is 9, and w varies directly with z, what is the value for z when w is 5?
Answer:
3 cuh
Step-by-step explanation:
15/3 = 5 9/3= 3