Surface area and volume
TIME: Time 1 hr
General Instructions:
Ø All Questions are compulsory.
Ø Marks are given alongwith the questions individually.
Ø Use of calculator is not permitted.

Q.1 The volume of a vessel in the form of a right circular cylinder is 448 cm3 and its height is 7cm. Find the radius of its base. (2)
Q.2 A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is of the curved surface of the whole cone, find the ratio of the line segment into which the cone’s altitude is divided by plane. (3)
Q.3 A well, whose diameter is 7m, has been dug 22.5m deep and the earth dug out is used to form an embankment 10.5m wide around it. Find the height of the embankment. (3)
Q.4 A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the solid, find how much more space it will cover. (3)
Q.5 A right circular triangle with sides 3cm and 4cm is revolved around its hypotenuse. Find the volume of the double cone thus generated. (5)
Q.6 The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be of the volume of the given cone, at what height above the base is the section made. (5)
Q.7 A hemispherical bowl of internal radius 9cm is full of liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 3cm and height 4cm. How many bottles are necessary to empty
the bowl? (3)
Q.8 The rain water from a roof 22m 20m drains into a cylindrical vessel having diameter of base 2m and height 3.5m. If the vessel is just full, find the rainfall in cm. (3)
Q.9 A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20m. The heights of the cylindrical and conical portions are 4.2m and 2.1m, respectively. Find the volume of the tent. (3)
Q.10 A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104cm and radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Re 1 per dm2. (5)