The plastic cylinder has a diameter of 2 cm. There is a rectangular 0.6 cm square prism through the middle of the cylinder, extending from the top to the bottom. The height of the cylinder is 6 cm. Find the volume of the cylinder without the prism.
Answers
Answer:
The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.
Step-by-step explanation:
The volume of the cylinder without the prism can be defined as the volume of the entire cylinder ([tex]V_{cy}[/tex]), measured in cubic centimeters, minus the volume of the prism ([tex]V_{pr}[/tex]), measured in cubic centimeters. That is:
[tex]V = V_{cy}-V_{pr }[/tex] (1)
[tex]V = \frac{\pi}{4}\cdot D^{2}\cdot h - l^{2}\cdot h[/tex]
[tex]V = \left(\frac{\pi}{4}\cdot D^{2}-l^{2} \right)\cdot h[/tex] (2)
Where:
[tex]D[/tex] - Diameter of the cylinder, measured in centimeters.
[tex]l[/tex] - Side of the square prism, measured in centimeters.
[tex]h[/tex] - Height of the square prism, measured in centimeters.
If we know that [tex]D = 2\,cm[/tex], [tex]l = 0.6\,cm[/tex] and [tex]h = 6\,cm[/tex], then the volume of the cylinder without the prism is:
[tex]V = \left[\frac{\pi}{4}\cdot (2\,cm)^{2}-(0.6\,cm)^{2} \right]\cdot (6\,cm)[/tex]
[tex]V \approx 16.690\,cm^{3}[/tex]
The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.
Related Questions
PLEASE
What is the solution to the equation 4 ( b − 2 ) − 10 = 2b + 6 ?
Answers
Step by step explanation:
First simplify both sides of the equation
( 4 )( b ) + ( 4 ) ( - 2 ) + -10 = 2b + 6 (distribute)
4b + -8 + -10 = 2b + 6
(4b) + (-8 + -10 ) = 2b + 6 (combine like terms)
4b + -18 = 2b + 6
4b - 18 = 2b + 6
Then subtract 2b from both sides
4b - 18 - 2b = 2b + 6 - 2b
2b - 18 = 6
After that you add 18 to both sides
2b - 18 + 18 = 6 + 18
2b = 24
2b/2 = 24/2
b = 12
find each unit price to decide which is the best buy
Answers
Answer:
do you have more info so I can help
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Answers
Answer:
92°=180°/y° I think this is correct
The y-intercept of the line whose equation is x - y = 7 is
7
1
-7
Answers
Answer:
-7
Step-by-step explanation:
x-y=7
-y=-x+7
y=x-7
hope it helps
Jayden drew a scale drawing of an arcade. He used the scale 1 inch = 3 feet. If an air hockey table is 3 inches long in the drawing, how long is the actual air hockey table?
Answers
Answer:
9 Feet
Step-by-step explanation:
Lets start with a ratio:
1:3
Now lets look at the other ratio:
3:?
If the 1 turned into a three in the second ratio, then what will the 3 in the first ratio turn into?
9!
Because 1x=3 should be equivalent to 3x=9
Lets check our work:
x=3
3x=9
Simplify by dividing by 3 on both sides:
x=3
x=3
It worked!
The answer is 9 feet. If the air hockey table is 3 inches long and 1 inch = 3 feet, 3 x 3 = 9.
This is something I have been trying forever !!!
Answers
Answer:45 degrees
Step-by-step explanation: The opposite angles theorem
Answer:
45
.................. . ...
Unfortunately, Fred had some trouble in the kitchen and 3/5 of the peanut butter cookies were burned. a. How many peanut butter cookies does Fred have left to sell?
Answers
Answer: 12 peanut butter cookies
Step-by-step explanation:
Fred had made 10 dozen cookies which means he made:
= 10 * 12
= 120 cookies
Out of those, 1/4 were peanut butter:
= 120 * 1/4
= 30 peanut butter cookies
He burned 3/5 of the peanut butter cookies:
= 30 * 3/5
= 18 cookies were burnt
The amount let is therefore:
= 30 - 18
= 12 peanut butter cookies
Point M is on line segment LN. Given MN = 3x, LN = 4x + 9, and
LM 2x + 7, determine the numerical length of LM.
Answers
Answer:
LM = 11 units
Step-by-step explanation:
Given M is on LN , then
LM + MN = LN , substitute values
2x + 7 + 3x = 4x + 9
5x + 7 = 4x + 9 ( subtract 4x from both sides )
x + 7 = 9 ( subtract 7 from both sides )
x = 2
Thus
LM = 2x + 7 = 2(2) + 7 = 4 + 7 = 11
I need help with this asap plzzz&thank u!!
Answers
Answer:
94hhfgkifc llo gfc bbn jdcjkydcjkufv
Which of the following points does not lie on the graph of y = 1/2x+3?
1) (10,8)
2) (0,3)
3) (-2,2)
4) (-6,-3)
Answers
Answer:
number 1 doesn't lie on the graph
Step-by-step explanation:
and I don't really have an explanation
(:
Consider the expressions given below. For each expression below, select the letter that corresponds to the equivalent expression from that given list.
Answers
Answer:
(4x³ - 4 + 7x) - (2x³ - x - 8) ----> B.
(-3x² + x⁴ + x) + (2x⁴ - 7 + 4x) ----> D.
(x² - 2x)(2x + 3) ----> A.
Step-by-step explanation:
.
How many grams are there in 55 kilograms? O A. 550 g O B. 5,500 g O C. 55,000 g O D. 550,000 g
can someone please help me :(
Answers
Answer:
The answer is C. 55,000
Step-by-step explanation:
Hope this helps ;)
42 slices from 3 cakes = 84 slices from____ cakes
Answers
6 Cakes man 6 cakes 42*2 3*2
Answer:
42 slices from 3 cakes = 84 slices from 6 cakesStep-by-step explanation:
Let the unknown value be x
[tex]42 = 3\\84 =x\\\\[/tex]
Cross Multiply
[tex]42\times x = 84\times 3\\\\42x = 252[/tex]
Divide both sides of the equation by 42
[tex]\frac{42x}{42} = \frac{252}{42} \\\\Simplify\\\\x =6[/tex]
URGENT PLEASE HELP Enter the value of (1/2) (-8) (4). Use the on-screen keyboard to enter the value in the box below.
Answers
Answer:-16
Step-by-step explanation:
-16 bc it is what it is
I need help I don't understand
Answers
Answer:
Step-by-step explanation:
Angle LPR and Angle PLN are supplementary to one another
9x+26+5x=180
Combine like terms
14x+26=180
Subtract 26 from both sides
14x=154
Divide 14 on both sides
x=11
Hope it helped :))
What expression -5+(-5r)+10
Answers
Can you help meh answer for brianliest
Answers
Answer:
1st One- 1 13/30
2nd One- 1 13/20
3rd One- 1/6
Step-by-step explanation:
Because yes
Answer:
1 13/30 1 13/20 1/6
Step-by-step explanation:
because i am smart
Sam plans to double his savings each day. He starts
with $0.03 in his account. How much will be have saved
after 30 days?
Answers
Answer:
$32212254.72Step-by-step explanation:
Initial value = $0.03Increase rate = 2 times each dayTime = 30 daysSaving amount after 30 days:
$0.03*2^30 = $32212254.72BlacIf w = -2 and v = -8, which of the following expressions shows the values correctly substituted in for the variables in the expression w2 - v + 1?
(-2) 2 - (-8) + 1
(-2) 2 - (8) + 1
-2 2 - (-8) + 1
-2 2 - 8 + 1
Answers
Answer:
-2² - (-8) + 1
Step-by-step explanation:
The values given are:
w = -2 and v = -8
Expression given:
w² - v + 1
When we substitute, we put a certain value in place of another. In an equation, variables are used as placeholders.
For this problem:
w = -2
v = -8
So;
-2² - (-8) + 1
Answer:
Given that w=-2 and v=-8
The expression is w²-v+1
Now putting the value of w=-2 and v=+8 in the given expression, we get
(-2)²-(-8)+1
Hence, (-2)²-(-8)+1 is the right answer.
How would the intervals of the solution set differ between a polynomial inequality and a rational inequality?
Answers
Answer:
Two differences: A polynomial inequality (PI) can always be replaced by a PI with one side zero. A rational inequality (RI) can not, because you do not know the sign of the denominator; a(x)b(x)>c(x)d(x) can not safely be replaced by a(x)d(x)−b(x)c(x)b(x)d(x)>0 because b(x) and/or d(x) might change signs unexpectedly.
Step-by-step explanation:
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
A.
n + n + 2 + n + 4 + n + 6 = –72; n = –21; n + 2 = –23; n + 4 = –25; n + 6 = –27
B.
n + (n – 2) + (n – 4) + (n – 6) = –72; n = – 21; n – 2 = –23; n – 4 = –25; n – 6 = – 27
C.
n – (n + 2) – (n + 4) – (n + 6) = –72; n = –20; n + 2 = –18; n + 4 = –16; n + 6 = –14
D.
n + n + 2 + n + 4 + n + 6 = –72; n = –21; n + 2 = –19; n + 4 = –17; n + 6 = –15
Answers
Answer:
D. n+n+2+n+4+6= -72; n= -21; n+2= -19; n+4= -17; n+6= -15
There are 2 below and 2 above it.
-15, -17, -19, -21
Step-by-step explanation:
the sum of four consecutive odd integers is -72. write an equation to model this situation, and find the values of the four integers .
n + n+2 + n+4 + n+6 = -72
4n + 12 = -72
or
-72/4 = -18, the center
Solve the area formula for a circle, A = πr2, for r2.
r2 = Aπ
r2 = A – π
Answers
Answer:
The solution of r² is r² = [tex]\frac{A}{\pi }[/tex]
Step-by-step explanation:
To solve an equation for one of its variables, do that
Separate the term of this variable on one side and the other terms on the other sidesMake the coefficient of the variable equals1 (if it is not 1)Let us solve the question
∵ The formula of the area of the circle is A = π r²
∵ The subject is r² ⇒ The variable which we need to solve for it
→ By using the 1st step up divide both sides by π to move it from the right
side to the left side
∵ [tex]\frac{A}{\pi }[/tex] = [tex]\frac{\pi r^{2}}{\pi }[/tex]
∴ [tex]\frac{A}{\pi }[/tex] = r²
→ Switch the two sides
∴ r² = [tex]\frac{A}{\pi }[/tex]
The graph of 3x − 2y = -1 is shown on the grid.
Answers
Answer:
slope: 3/2, y-intercept: (0,1/2)
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
In a certain chemical, the ratio of zinc to copper is 3 to 13 . A jar of the chemical contains 585 of copper. How many grams of zinc does it contain?
Answers
Answer: 135 grams of Zinc
Step-by-step explanation:
The ratio of Zinc to Copper in this scenario is 3:13 and in this jar there is 585 of Copper.
Using direct proportion, the grams of Zinc in the jar is:
3 : 13
x : 585
Cross -multiplying will give:
1,755 = 13x
x = 1,755/13
x = 135 grams of Zinc
Someone please help me with thiss
Answers
Answer:
The total trip will be 4 hours long.
Step-by-step explanation:
The length of the trip decreases by 65/2 miles for every half hour. So in 2 half hours (or 1 hour), Aubree would have traveled the last 65 miles she needed.
Jacy paid $15.48 to download 12 songs last month. She paid the same amount for each song and also had to spend $5.04 to enroll in the music purchasing program.
Part A
Let s represent the amount that Jacy paid for each song she downloaded.
Which equation could you use to find the value of s?
12s = 15.48
15.48 + s = 12 + 5.04
12 + s = 15.48 + 5.04
12s + 5.04 = 15.48
Answers
Hope this helps!
Have a nice day :)
The solution is, 12s + 5.04 = 15.48, is the equation which could you use to find the value of s.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
given that,
Jacy paid $15.48 to download 12 songs last month.
She paid the same amount for each song and also had to spend $5.04 to enroll in the music purchasing program.
now, we have,
Let s represent the amount that Jacy paid for each song she downloaded.
so, we get,
She paid the same amount for each song and also had to spend $5.04 to enroll in the music purchasing program.
i.e. 12s + 5.04
and, Jacy paid $15.48
i.e. the equation which could you use to find the value of s is,
12s + 5.04 = 15.48
Hence, The solution is, 12s + 5.04 = 15.48, is the equation which could you use to find the value of s.
To learn more on equation click:
brainly.com/question/24169758
#SPJ2
Please help!! I will mark you brainliest
Answers
Answer:
8x-3=5x+6
Step-by-step explanation:
8x-3=5x+6
3x=9
x=3
If you could help I would really appreciate it, but if not that’s fine. Thank you.
Answers
2•(7) -7
14-7
7
The answer is 7!
can you solve for x and y pls hurry ...
Answers
Answer:
x=50 y=25
Step-by-step explanation:
brainliest pls
A 6-сm long toy car is 4% of the length of the official scale model of the Batmobile. How long is the official scale model? Show your work (you may use a linear model if you'd like)
Answers
Answer:
[tex]150\:\mathrm{cm}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] represent the length of the official scale model. We can set up the following proportion:
[tex]x\cdot 0.04=6[/tex].
Solving, we get:
[tex]x=\frac{6}{0.04}=\fbox{$150\:\mathrm{cm}$}[/tex].