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
kirill [66]
2 years ago
10

a cone is constructed by cutting a sector from a circular sheet of metal with radius . the cut sheet is then folded up and welde

d. find the radius and height of the cone with maximum volume that can be formed in this way.
Physics
1 answer:
Svet_ta [14]2 years ago
3 0

The expression for the radius and height of the cone can be obtained from

the property of a function at the maximum point.

  • The \ radius, \ of \ the \ base \ of \ the \ cone \ is \ \sqrt{ \dfrac{3}{4}} \times radius \ of \ circular \ sheet \ metal
  • The height of the cone is half the length of the radius of the circular sheet metal.

Reasons:

The part used to form the cone = A sector of a circle

The length of the arc of the sector = The perimeter of the circle formed by the base of the cone.

Volume \ of \ a \ cone = \dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot h

  • Volume \ of \ a \ cone, \, V = \dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot \sqrt{(s^2- r^2)}

θ/360·2·π·s = 2·π·r

Where;

s = The radius of he circular sheet metal

h = s² - r²

  • \dfrac{dV}{dr} = \dfrac{d}{dr}  \left(\dfrac{1}{3} \cdot  \pi \cdot r^3 \cdot \sqrt{(s^2- r^2)}\right) = \dfrac{\pi \cdot (3 \cdot r^2 \cdot  s^2 - 4 \cdot r^4)}{\sqrt{(s^2- r^2)}} = 0

3·r²·s² - 4·r⁴ = 0

3·r²·s² = 4·r⁴

3·s² = 4·r²

\underline{\left  \right. The \ radius, \, r =\sqrt{ \dfrac{3}{4}} \cdot s}

\underline{The \ height, \, h =\sqrt{s^2 - \dfrac{3}{4}\cdot s^2} = \dfrac{s}{2}}}

Learn more here:

brainly.com/question/14466080

You might be interested in
Mars, which has a radius of 3.4 × 106 m and a mass of 6.4 × 1023 kg, orbits the Sun, which has a mass of 2.0 × 1030 kg at a dist
Arisa [49]

The correct answer is: revolution

6 0
3 years ago
Read 2 more answers
Which of the following equations is balanced correctly? A. 3 H2O → H2 + 3 O2 B. Cl2 + 2 KBr → KCl + Br2 C. 2 C2H2 + 5 O2 → 4 CO2
posledela
A. the carbons are unbalanced B. the hydrogens are unbalanced. D. the chlorines are unbalanced. That leaves C. to be correctly balanced.
8 0
3 years ago
Read 2 more answers
What is true about energy that is added to a closed system?
Setler [38]

The correct answer is B

6 0
3 years ago
Read 2 more answers
Mali loves to make herself dizzy. She spins in place 7 times before falling down right where she was standing. Find her distance
Mila [183]
The answer is 0 bc she didint move
Explanation:
8 0
3 years ago
Read 2 more answers
A student is building a simple circuit with a battery, light bulb, and copper wires. When she connects the wires to the battery
denis23 [38]
It’s will be B because the circuit had a open or close so if that doesn’t work than it’s because it’s open
5 0
3 years ago
Read 2 more answers
Other questions:
  • An astronaut on a small planet wishes to measure the local value of g by timing pulses traveling down a wire which has a large o
    13·1 answer
  • Dos cargas iguales de 10^-7C estan separadas por una distancia de 2m. calcule la fuerza con que se repelen
    10·1 answer
  • X rays have wavelengths on the order of 1 3 10210 m. calcu‑ late the energy of 1.0 3 10210 m x rays in units of kilojoules per m
    8·1 answer
  • What structure on the south african coast has a range of 63 km and releases flashes every 30 seconds?
    9·1 answer
  • At one particular moment, a 19.0 kg toboggan is moving over a horizontal surface of snow at 3.60 m/s. After 6.75 s have elapsed,
    13·1 answer
  • Examine the scenario. Object A has 5 protons and 5 electrons. Object B has 5 protons and 7 electrons. Which option most accurate
    12·1 answer
  • Which one of the following is an example of an indicator?
    7·1 answer
  • Physics help please..............
    11·1 answer
  • Taylor Swift weighing 794 N gets on an elevator. The elevator uses 313 W of power to lift the person 22.0 m. How much time did t
    5·1 answer
  • What chemical formula did early instigators assume for water?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!