1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vesna [10]
3 years ago
11

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =

0, x = 5, x = 7; about x = 1
Mathematics
1 answer:
miss Akunina [59]3 years ago
6 0

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid.  When we rotate it about x = 1, we get a hollow cylinder shape.  We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part.  If we use shell method, we only need one integral.  So let's use shell method.

Cut a thin, vertical slice of the region.  The width of this slice is dx.  The height of the slice is y₂ − y₁ = x − 0 = x.  The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

You might be interested in
Select the correct answer.
dem82 [27]

Answer:

C

Step-by-step explanation:

The ratio 11:16 cannot be simplified

3 0
3 years ago
Read 2 more answers
Which expression is equivalent to 2/3(6x+3)
irina1246 [14]
2/3(6x+3)
2/3 x 3(2x+1)
2(2x+1)
4x+2
Therefore your answer is 4x+2
5 0
3 years ago
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Tra
ch4aika [34]

Answer: The answer is the second one/b.

7 0
3 years ago
Read 2 more answers
Someone please help!! I’ll give brainliest:))
Allisa [31]
I’ve attached my work...
Hope it helps! Have a nice day :)

8 0
3 years ago
Please help me please will give brainliest to anyone who is good​
hichkok12 [17]

Answer:

C

Step-by-step explanation:

N = st

Number of toothpicks = (number of students) x (toothpicks)

5 0
3 years ago
Read 2 more answers
Other questions:
  • The volume of the oblique cylinder is 24 ft^3. Which statements are true? Check all that apply.
    11·2 answers
  • Trig please help.
    12·1 answer
  • The graphs of f(x) and g(x) are shown below:
    6·1 answer
  • If an= 4+2(n-1), what is the first term?
    6·1 answer
  • A coffee maker priced at $189.99 is on sale for 20% off but then sales tax of 9% and 8% are added to the price after discount. W
    6·1 answer
  • Find the nth term of this quadratic sequence <br> 2, 8, 18, 32, 50,
    5·1 answer
  • Which shape has 4 lines of symetry?
    15·2 answers
  • Determine whether quadrilateral EFGH is similar to quadrilateral QRST. If so, give the similarity statement. (ASAP PLS HELP!! no
    12·1 answer
  • Please help with this, thank you.
    10·1 answer
  • 968 ÷ 38 help me now plzzz
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!