The largest area of the trapezium inscribed in a semi-circle or radius `R ,` if the lower base is on the diameter, is `(3sqrt(3))/4R^2` (b) `(sqrt(3))/2R^2` `(3sqrt(3))/8R^2` (d) `R^2`

Three circles of radius 1 cm are circumscribed by a circle of radius r, as shown in the figure. Find the value of r? (a) sqrt(3) + 1 (b) (2+sqrt(3))/(sqrt(3)) (c) (sqrt(3) + 2)/(sqrt(2)) (d) 2 + sqrt(3)

A cone is circumscribed about a sphere of radius R.The volume of the cone is minimum if its height is: (A) 3R(B)4R(C)5R(D)2sqrt(2)R

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6sqrt(3)r.

A rectangle is inscribed in an equilateral triangle of side length 2a units.The maximum area of this rectangle can be sqrt(3)a^(2)(b)(sqrt(3)a^(2))/(4)a^(2)(d)(sqrt(3)a^(2))/(2)

The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius rcm is (2)/(sqrt(3))r^(2)( b) (4)/(3)r^(2)(c)(8)/(3sqrt(3))r^(3)(d)(1)/(3sqrt(3))r^(3)

Three equal circles each of radius r touch one another.The radius of the circle touching all the three given circles internally is (2+sqrt(3))r(b)((2+sqrt(3)))/(sqrt(3))r((2-sqrt(3)))/(sqrt(3))r(d)(2-sqrt(3))r

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

In the given figure,ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r .Which of the following is the area of the triangle? (r+DE)^((1)/(2))(r-DE)^((3)/(2))(b)(r-DE)^((1)/(2))(r+DE)^(2)(c)(r-DE)^((1)/(2))(r+DE)^(2)(d)(r-DE)^((1)/(2))(r+DE)^((3)/(2))(d)

A solid metallic sphere of radius r is converted into a solid right circular cylinder of radius R . If the height of the cylinder is twice the radius of the sphere,then R=r( b) R=r sqrt((2)/(3))(c)R=sqrt((2r)/(3))(d)R=(2r)/(3)