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
A 103 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 93 m below
siniylev [52]

Answer:

125.83672 seconds

Explanation:

P = Power of the horse = 1 hp = 746 W (as it is not given we have assumed the horse has the power of 1 hp)

m = Mass of professor = 103 kg

g = Acceleration due to gravity = 9.8 m/s²

h = Height of professor = 93 m

Work done would be equal to the potential energy

W=mgh\\\Rightarrow W=103\times 9.8\times 93\\\Rightarrow W=93874.2\ J

Power is given by

P=\frac{W}{t}\\\Rightarrow t=\frac{W}{P}\\\Rightarrow t=\frac{93874.2}{746}\\\Rightarrow t=125.83672\ seconds

The time taken by the horse to pull the professor is 125.83672 seconds

6 0
3 years ago
A 65-kg ice skater stands facing a wall with his arms bent and then pushes away from the wall by straightening his arms. At the
Marrrta [24]

Our values can be defined like this,

m = 65kg

v = 3.5m / s

d = 0.55m

The problem can be solved for part A, through the Work Theorem that says the following,

W = \Delta KE

Where

KE = Kinetic energy,

Given things like that and replacing we have that the work is given by

W = Fd

and kinetic energy by

\frac {1} {2} mv ^ 2

So,

Fd = \frac {1} {2} m ^ 2

Clearing F,

F = \frac {mv ^ 2} {2d}

Replacing the values

F = \frac {(65) (3.5)} {2 * 0.55}

F = 723.9N

B) The work done by the wall is zero since there was no displacement of the wall, that is d = 0.

6 0
2 years ago
Water at the top of a slope has potential energy. true or false
ASHA 777 [7]
<span>The statement is TRUE. Water does have potential energy at the top of a slope. The reason why is that potential energy is energy possessed by a body based on its position relative to a zero point. In this case, water at the top of the slope is at an elevation above ground (zero point). The energy is not kinetic (moving) energy since the water is not moving.</span>
8 0
3 years ago
Read 2 more answers
A net force is acting on an object. The object is moving in a
Hoochie [10]

Answer:

The object's velocity would increase due to the change in force.

Explanation:

4 0
2 years ago
El resultado de pasar a notación científica la cifra 2 000 000 000 · 10 -15
tensa zangetsu [6.8K]
19,999,985 nomas creo y soy positivo que si es pero puedes ablar ingles
6 0
2 years ago
Other questions:
  • George determines the mass of his evaporating dish to be 3.375 g. He adds a solid sample to the evaporating dish, and the mass o
    13·1 answer
  • If a wheel falls from an airplane that is flying horizontally at an altitude of 500 m, how long will it take for the wheel to st
    14·1 answer
  • The voltage across a membrane forming a cell wall is 72.7 mV and the membrane is 9.22 nm thick. What is the magnitude of the ele
    5·1 answer
  • How do contact forces such as friction differ from gravitational and magnetic forces?
    13·1 answer
  • A student leaves a sidewalk corner walks 3.0 blocks north then walks 3.0 blocks west.what is the students displacement from the
    8·1 answer
  • How did the Planck mission help scientists learn about the age of the universe
    8·1 answer
  • Light travels in...<br> A) electromagnetic waves B) electrons <br> C) photons <br> D) a and c
    13·1 answer
  • A swift moving hawk is moving due west with a speed of 30 m/s; 5.0 s later it is moving due north with a speed of 20 m/s.
    11·1 answer
  • Please help me I have to send for my teacher​
    14·1 answer
  • A ball is thrown at an angle of 38 degrees to the horizontal. What happens to the magnitude of the ball's vertical acceleration
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!