A semicircular thin sheet of metal of diameter 30 cm is bent an open an conical cup is made. Find the capacity of the cup.

A semi circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

A wire is in the form of a circle with diameter 21 cm. It is cut and bent into a square. Find the area of the square.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.

A rectangular sheet of paper of dimensions 30 cmxx16 cm can be transformed into an open ended cylinder in two ways. Find the ratio of volumes of two cylinders thus formed.

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square tin sheet of side length a feet and then folding up the flaps. Find the side of the square cut-off.

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig. 13.23). The diameters of die two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, Find the volume of water the bucket can hold. (Take pi=22/7 ).

A spherical convex surface of radius of curvature 20 cm, made of glass (mu=1.5) is placed in air. Find the positon of the image formed, if a point object is placed at 30 cm in front of the convex surface on the principal axis.

An oil funnel made of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

A soft drink is avaliable in two packs a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Find the container's capacity and how much ?