If `h , c ,V` are respectively the height, the curved surface and the volume of a cone, prove that `3piV h^3-C^2h^2+9V^2=0.`

If h ,\ S\ a n d\ V denote respectively the height, curved surface area and volume of a right circular cone, then 3piV h^3-\ S^2h^2+9V^2 is equal to (a) 8 (b)0(c) 4pi (d) 32pi^2

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

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h . If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is (a) 2h (b) (2h)/3 (c) (3h)/2 (d) 4h

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h . If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is 2h (b) (2h)/3 (c) (3h)/2 (d) 4h

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is (a) 3 V (b) 4 V (c) 6 V (d) 8 V

V =1/3 pi ((d)/(2)) ^(2) h A circle of rubber with a constant diameter d is placed on a table, its perimeter is anchored to the table and a string is attached to its centre. When the string is pulled upwards, a cone is formed with height h and volume V. The relationship between d, h, and V is represented above. Which of the following statements must be true ? I. As the volume of the cone decreases, the height also decreases. II. If the diameter of the base of the cone is 6 centimeters, the height can be determined by dividing the volume by 3pi. III. If the height of the conc triples, the volume must also triple.

The area of two holes A and B are 2a and a , respectively, The holes are at height (H//3) and (2H//3) from the surface of water. Find the correct option(s):

From a given solid cone of height H, another inverted cone is carved whose height is h such that its volume is maximum. Then the ratio H/h is

The difference between the value of C_p of H_2 and C_v of He will be

The height h of cylinder equals the circumference of the cylinder. In terms of h , what is the volume of the cylinder? (a) (h^3)/(4pi) (b) (h^2)/(2pi)\ (c) (h^3)/2 (d) pih^3