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
goldfiish [28.3K]
3 years ago
11

A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 505π ft3,

determine the radius and height of the silo that requires the least amount of material to build. Hint: The volume of the silo is πr2h + 2 3 πr3, and the surface area (including the floor) is π(3r2 + 2rh). (Round your answers to one decimal place.)
Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
7 0

Answer:

radius   x  = 3 ft

height   h = 23,8  ft

Step-by-step explanation:

From problem statement

V(t)  = V(cylinder) + V(hemisphere)

let x be radius of base of cylinder (at the same time radius of the hemisphere)

and h the height of the cylinder, then:

V(c)  = π*x²*h       area of cylinder = area of base + lateral area

                                              A(c)  = π*x²  +   2*π*x*h

V(h) = (2/3)*π*x³   area of hemisphere   A(h)  =   (2/3)*π*x²

A(t)  =  π*x²  +   2*π*x*h +   (2/3)*π*x²

Now A as fuction of x    

total volume   505  = π*x²*h  +  (2/3)*π*x³

h = [505 - (2/3)* π*x³ ]  /2* π*x    

Now we have the expression for A as function of x

A(x) =  3π*x² + 2π*x*h     A(x) = 3π*x² + 505  - (2/3)π*x³

Taking derivatives both sides

A´(x) =  6πx -  2πx²              A´(x) =  0         6x  - 2x²  = 0

x₁  =  0  we dismiss

6 - 2x = 0

x = 3     and   h = [505 - (2/3)* π*x³]/2* π*x

h  =  (505 - 18.84) / 6.28*3

h  = 23,8  ft

You might be interested in
What is the cube root of 57 R cubed
Studentka2010 [4]
Approximately 3.849 is the cube root of 57 cube root.
8 0
3 years ago
Which is NOT used to reach conclusion in a formal proof?
Sav [38]
The answer is Inductive Reasoning


3 0
3 years ago
cindy is training for a race. she ran 3/5 mile each day for 7 days. how many miles did she ran in those 7 days
anyanavicka [17]
Multiply the two numbers

3/5*7/1= 21/5

21/5= 4 1/5 miles

Answer: 4 1/5 miles
3 0
3 years ago
The period of the function y=sin(1/4 x) is equal to
Aleonysh [2.5K]

Answer:

8*\pi

8 0
2 years ago
What expression gives the distance between the points (4,6) and (7,-3)?
solniwko [45]

Answer:

\sqrt{(-3^2-6)+(7^2-4^2)}

Step-by-step explanation:

Use the form: \sqrt{(x^2-x^1)+(y2-y1)^2

so: \sqrt{(-3^2-6)+(7^2-4^2)}

6 0
3 years ago
Other questions:
  • The volume of a box V is given by the formula V=lwh, where l is the length, w is the width and h is the height. Solve the formul
    12·2 answers
  • Administrators surveyed students enrolled in a new school in order to choose the school mascot. there are 480 students enrolled
    15·2 answers
  • last season a baseball player scored 14 runs in 18 games. this season the player scored 12 runs in 15 games. find the number of
    9·1 answer
  • 5.7 is increased to 7.8<br> What is the percentage of increase?
    9·2 answers
  • you deposit $1050 into an account that pays 7.25% interest per year. find the amount after six year given the following: a) comp
    9·1 answer
  • Do these pairs of values (x and y) represent two quantities that are
    6·1 answer
  • On a coordinate grid, point P is at (4, 3) and point R is at (−2, −5). Points Q and S are a reflection of both points across the
    14·1 answer
  • calculate the simple interest and compound interest on ₹5000 for 2 years at 10% per annum. how much more is the compound interes
    9·1 answer
  • the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . wri
    5·1 answer
  • What are the odds of two threes being rolled by two 6-sided dice?<br><br> 1/?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!