Show that the semi-vertical angle of th...

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `tan^(-1)sqrt(2)`.

A

` tan^(-1)2`

B

` cot ^(-1)2`

C

`tan ^(-1) sqrt2`

D

`cot^(-1)sqrt2`

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

APLICATIONS OF DERIVATIVES
MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - I : CHAPTER 12)|19 Videos
APLICATIONS OF DERIVATIVES
MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - II : CHAPTER 12)|19 Videos
APPLICATIONS OF DEFINITE INTEGRALS
MARVEL PUBLICATION|Exercise TEST YOUR GRASP|11 Videos

Similar Questions

Explore conceptually related problems

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is cos^(-1)(1)/(sqrt(3))

Show that the semi - vertical angle of the right - circular cone of maximum volume and of given slant height is : (i) tan^(-1)sqrt2 (ii) cos^(-1)""(1)/(sqrt3).

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is cot^(-1)(sqrt(2))

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is (1)/(3)h

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin^(-1)((1)/(3))

show that the semi vertical angle of a right circular cone of given total surface area and max volume is sin ^(-1)((1)/(3))

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12cm is 16cm.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2(R)/(sqrt(3)) .Also find maximum volume.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) Also find the maximum volume.

The height of the cone of maximum volume inscribed in a sphere of radius R is

MARVEL PUBLICATION-APLICATIONS OF DERIVATIVES-MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - II : CHAPTER 12)

Show that the semi-vertical angle of the cone of the maximum volume a...
Text Solution
|
If S=16+ 192 t-t^(3), then distance tavelled by the particle before co...
Text Solution
|
The distances moved by a particle in time t seconds is given by s=t^(3...
Text Solution
|
A stone thrown vertically upwards rises S ft in t seconds where S =11...
Text Solution
|
If displacement x at time t is x=sqrt(1+t^(2)) , then acceleration is
Text Solution
|
If the circumference of a circle at the rate of 0.2 cm //sec, then, wh...
Text Solution
|
A stone is dropped into a quiet pond and waves spread in the form of c...
Text Solution
|
Perimeter of square increases at the rate of 0.4 cm// sec. When the si...
Text Solution
|
Each side of an equilateral triangle increases at a uniform rate of 0....
Text Solution
|
If the surface area of a cube increases at the rate of 0.6cm^(2) //sec...
Text Solution
|
If V denotes the volume and S is the surface area of a sphere. If radi...
Text Solution
|
Water is poured into an inverted cone of semi-vertical angle 30^(@) at...
Text Solution
|
A ladder 10 m long leans against a house. When its foot is 6 m from th...
Text Solution
|
If y=(log x) - (2)/(x), x=(1)/(2), deltax =10 ^(-8), then delta y ~~…
Text Solution
|
If 1^(@) =0.0174^(c), then tan (45^(@) 50')~~…
Text Solution
|
If diameter of a sphere is 2 cm with error 0.082 mm, then approximate ...
Text Solution
|
If a wire of length l, with error delta l, is bent into an equilatera...
Text Solution
|
if radius of a sphere is r with error delta r , and S is its surface ...
Text Solution
|
If 1^(@) =0.018^(c), then sin^(2) (45 ^(@) 2')~~…
Text Solution
|
A point P moves along the curve y=x^(3). If its abscissa is increasing...
Text Solution
|