Long Answer Type
of the volume of the sphere.Let R be the radius of cone, r be the radius of sphere and OD = x
∴ height of cone i.e. h = x + r
Now x2 + R2 = r2 ⇒ R2 = r2 – x2 ...(1)
Let V be the volume of cone.
Now x = – r is not possible as x cannot be negative.
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is 
For a given current surface area of right circular cone when the volume is maximum. Prove that the semi-vertical angle is 
where 
Short Answer TypeProve that a conical tent of given capacity will require the least amount of convas when the height is 
times the radius of the base.
Show that the right circular cone of least curved surface and given volume has an altitude equal to an altitude equal to 
times the radius of the base.
Long Answer TypeFind the altitude of a right circular cone of maximum curved surface which can be inscribed in a sphere of radius r.
Find the equation of the line through the point (3, 4) which cuts from the first quadrant a triangle of minimum area.
Prove that the area of a right angled triangle of given hypotenuse is maximum when the triangle is isosceles.
Prove that the perimeter of a right-angled triangle of given hypotenuse equal to 5 cm is maximum when the triangle is isosceles.
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