Two cylindrical cans of radii `15 ~cm`, `10 ~cm` and heights `25 ~cm, 18 ~cm` are filled with oil. Both cans are emptied into another cylindrical can and the oil level reaches `30 ~cm` in. the new can. What is the radius of the new can?

a) Radius of a cylinder is 10 cm and its height is 5 cm . Find the base area and the curved surface area of the cylinder. b) The curved surface area of a cylinder is equal to its base area and its height is 12 cm . What is its radius?

A uniform field equal to 1.5T exists in a cylindrical region of radius 10.0cm, its direction parallel to the axis along east to west. A wire carrying current 7.0A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if : the wire intersects the axis.

A copper block length 5 cm , breadth 4 cm and thickness 2 cm is melted and made into a cylindrical rod of radius 2 mm . What is the length of the rod?

The radius of a cylinder increases at a rate of 1 cm/s and its height decreases at a rate of 1cm/s. Find the rate of change of its volume when the radius is 5 cm and the height is 15 cm. If the volume should not change even when the radius and height are changed, what is the relation between the radius and height?

Two parallel chords in a circle of diameter 30 cm have lengths 24cm and 18 .cm If the chords are on the same side of the centre, what is the distance between them? If the chords are on either side-of the centre, what is the difference between them?

Of all the closed cylindrical cans (right circular) of a given volume of 100 cubic. cm. find the dimensions of the can which has the minimum surface area.